- published: 22 Sep 2015
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In mathematics, a Lie group /ˈliː/ is a group that is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure. Lie groups are named after Sophus Lie, who laid the foundations of the theory of continuous transformation groups. The term groupes de Lie first appeared in French in 1893 in the thesis of Lie’s student Arthur Tresse, page 3.
Lie groups represent the best-developed theory of continuous symmetry of mathematical objects and structures, which makes them indispensable tools for many parts of contemporary mathematics, as well as for modern theoretical physics. They provide a natural framework for analysing the continuous symmetries of differential equations (differential Galois theory), in much the same way as permutation groups are used in Galois theory for analysing the discrete symmetries of algebraic equations. An extension of Galois theory to the case of continuous symmetry groups was one of Lie's principal motivations.
Group may refer to:
A lie is a statement that is known or intended by its source to be misleading, inaccurate, or false. The practice of communicating lies is called lying, and a person who communicates a lie may be termed a liar. Lies may be employed to serve a variety of instrumental, interpersonal, or psychological functions for the individuals who use them. Generally, the term "lie" carries a negative connotation, and depending on the context a person who communicates a lie may be subject to social, legal, religious, or criminal sanctions. In certain situations, however, lying is permitted, expected, or even encouraged. Because believing and acting on false information can have serious consequences, scientists and others have attempted to develop reliable methods for distinguishing lies from true statements.
As defined by Sartre, "bad faith" is lying to oneself. Specifically, it is failing to acknowledge one's own ability to act and determine one's possibilities, falling back on the determinations of the various historical and current totalizations which have produced one as if they relieved one of one's freedom to do so.
In mathematics, a Lie algebra (/liː/, not /laɪ/) is a vector space together with a non-associative multiplication called "Lie bracket" . It was introduced to study the concept of infinitesimal transformations. Hermann Weyl introduced the term "Lie algebra" (after Sophus Lie) in the 1930s. In older texts, the name "infinitesimal group" is used.
Lie algebras are closely related to Lie groups which are groups that are also smooth manifolds, with the property that the group operations of multiplication and inversion are smooth maps. Any Lie group gives rise to a Lie algebra. Conversely, to any finite-dimensional Lie algebra over real or complex numbers, there is a corresponding connected Lie group unique up to covering (Lie's third theorem). This correspondence between Lie groups and Lie algebras allows one to study Lie groups in terms of Lie algebras.
A Lie algebra is a vector space over some field F together with a binary operation called the Lie bracket that satisfies the following axioms:
Lie to Me (stylized as Lie to me*) is an American crime drama television series. It originally ran on the Fox network from January 21, 2009 to January 31, 2011. In the show, Dr. Cal Lightman (Tim Roth) and his colleagues in The Lightman Group accept assignments from third parties (commonly local and federal law enforcement), and assist in investigations, reaching the truth through applied psychology: interpreting microexpressions, through the Facial Action Coding System, and body language.
In May 2009, the show was renewed for a second season consisting of 13 episodes; Season two premiered on September 28, 2009. On November 24, 2009, Fox ordered an extra nine episodes for season two, bringing the season order to 22 episodes.
On May 12, 2010, Entertainment Weekly reported that Lie to Me received a 13-episode third season pick-up. The third season of Lie to Me was originally set to premiere on November 10, 2010. On September 28, 2010, the date was moved up to October 4, 2010, because of the cancellation of Lone Star.Lie to Me was officially canceled by Fox on May 11, 2011.
This is from a series of lectures - "Lectures on the Geometric Anatomy of Theoretical Physics" delivered by Dr.Frederic P Schuller
The first in a series of 4 lectures on Lie groups and Lie algebras (with a particular focus on physics) given by Gang Xu, a PSI Fellow, at the 2014-2015 PSI. This lecture provides an introduction to the subject, going through the motivation and basic examples/properties. If you're having trouble seeing the board at any point in the lectures, you can check out this pdf with snapshots of the board -- one shot for each change that occurs: http://pirsa.org/pdf/loadpdf.php?pirsa_number=14080028 These are NOT my videos! All rights, credit, etc. go to the Perimeter Institute, which can be found at the website linked to below. All the videos come from, and can be downloaded from in various formats and from previous years, the Perimeter Institute (where these lectures took place) website: http:...
A very short discussion on Lie Algebra within the context of applications in quantum physics. In particular, our context is angular momentum.
During the 19th century, group theory shifted from its origins in number theory and the theory of equations to describing symmetry in geometry. In this video we talk about the history of the search for simple groups, the role of symmetry in tesselations, both Euclidean, spherical and hyperbolic, and the introduction of continuous groups, or Lie groups, by Sophus Lie. Along the way we meet briefly many remarkable mathematical objects, such as the Golay code whose symmetries explain partially the Mathieu groups, the exceptional Lie groups discovered by Killing, and some of the other sporadic simple groups, culminating with the Monster group of Fisher and Greiss. The classification of finite simple groups is a high point of 20th century mathematics and the cumulative efforts of many mathe...
Lecture from 2016 upper level undergraduate course in particle physics at Colorado School of Mines
Complete playlist here: https://www.youtube.com/playlist?list=PLMsmpuzEhclYcPYi1wvDuigA41j6-genF
This is the second video in this lecture on simple groups, Lie groups and manifestations of symmetry. During the 19th century, the role of groups shifted from its origin in number theory and the theory of equations to its role in describing symmetry in geometry. In this video we talk about the history of the search for simple groups, the role of symmetry in tesselations, both Euclidean, spherical and hyperbolic, and the introduction of continuous groups, or Lie groups, by Sophus Lie. Along the way we meet briefly many remarkable mathematical objects, such as the Golay code whose symmetries explain partially the Mathieu groups, the exceptional Lie groups discovered by Killing, and some of the other sporadic simple groups, culminating with the Monster group of Fisher and Greiss. The class...
Complete playlist here: https://www.youtube.com/playlist?list=PLMsmpuzEhclYcPYi1wvDuigA41j6-genF
Introduction to Lie Algebras We will go over the basics of structure and representation theory of finite dimensional complex Lie algebras. We will define basic concepts as ideals, homomorphisms, representations, etc. Then we will move to structure theory of semisimple Lie algebras: Killing form, Casimir elements, root systems, classification of simple algebras. And finally we will go to the basics of representation theory: characters, Weyl formulas, etc. Even though we will try to keep it purely algebraic (1) and we may mention some connections to Lie Group theory and geometry (2). The only previous knowledge that this class will assume is some familiarity with basic algebraic objects like rings and fields. Understanding the notion of manifold would be useful when making connections to Li...
This is from a series of lectures - "Lectures on the Geometric Anatomy of Theoretical Physics" delivered by Dr.Frederic P Schuller
A representation (character) of a compact Lie group, restricted to the "Kostant principal SU₂" has a weight spectrum which can be interpreted as a sound. Here we listen to the sound thus produced by various representations of various Lie groups (the frequency is set so that the fundamental representation of SU₂ maps to 110Hz, or the A note of the second octave). All compact simple Lie groups up to rank 7 have been included, and for each one, every fundamental representation and the adjoint representation.
Physicist Carlos Perelman gave a series of lectures on lie algebra to Quantum Gravity Research's team of research scientists. We thought it would be useful for anyone interested in learning more about lie algebra. Quantum Gravity Research is a team of physicists, mathematicians and chemists, hard at work on “Emergence Theory,” a new quantum gravity theory (or “Theory of Everything”) that unifies space, time, energy, matter, information and consciousness. The group was founded by its director, Klee Irwin, and operates in Los Angeles as a non-for-profit organization.
Pour en savoir plus sur Paul Ekman (consultant pour la série "Lie to me") et sur ses formations, visitez notre site : http://www.detegogroup.eu/methodes-outils/paul-ekman-phd/ Arnaud Blavier (MD of Detego Group -- Learn to read people, based in Luxembourg) was interviewed live on Air TV (France) in May 2012 about the science behind the series « Lie to me » and the related Paul Ekman approved trainings. Learn how to read emotions and deceit in others through micro and subtle facial expressions and 4 other communication channels based on the science behind the hit Sky 1 TV, M6 and RTL-TVI series "Lie to me". If you'd like to find out more about this fascinating subject and the Paul Ekman approved courses then contact the team by e-mail: contact@detegogroup.eu or visit our website: http:/...
In mathematics, a Lie group is a group that is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure. Lie groups are named after Sophus Lie, who laid the foundations of the theory of continuous transformation groups. The term groupes de Lie first appeared in French in 1893 in the thesis of Lie’s student Arthur Tresse, page 3. Lie groups represent the best-developed theory of continuous symmetry of mathematical objects and structures, which makes them indispensable tools for many parts of contemporary mathematics, as well as for modern theoretical physics. They provide a natural framework for analysing the continuous symmetries of differential equations, in much the same way as permutation groups are used in Galois theory for a...
Garrett Lisi at FQXi's 5th International Conference.
Zhiwu Huang; Chengde Wan; Thomas Probst; Luc Van Gool In recent years, skeleton-based action recognition has become a popular 3D classification problem. State-of-the-art methods typically first represent each motion sequence as a high-dimensional trajectory on a Lie group with an additional dynamic time warping, and then shallowly learn favorable Lie group features. In this paper we incorporate the Lie group structure into a deep network architecture to learn more appropriate Lie group features for 3D action recognition. Within the network structure, we design rotation mapping layers to transform the input Lie group features into desirable ones, which are aligned better in the temporal domain. To reduce the high feature dimensionality, the architecture is equipped with rotation pooling la...
Lecture from 2018 upper level undergraduate course in particle physics at Colorado School of Mines. You can follow along at: http://inside.mines.edu/~aflourno/Particle/423.shtml
Today I have the latest numbers from the month of October in our Baltimore metro market and I’m going to compare them to last year’s numbers to see where things are headed to close out 2017. Year over year, the median sale price rose 2.8%. The total sales volume across the Baltimore metro area rose 0.5%. Along with these increases, the number of new listings rose 8.1%. To find out what these numbers mean going forward, watch my latest video. Learn more: https://www.discoverbaltimorerealestate.com/blog/the-numbers-dont-lie-a-shift-may-be-happening-soon-in-our-market/ About: The Lobas Group | Keller Williams is Greater Baltimore's most innovative real estate team. Contact: 8015 Corporate Dr., Nottingham, MD 21236 410-821-1199 TRANSCRIPTION: The October 2017 numbers are in from our Bal...
Learn dances step by step: visit AmnaDance.com, click on 'Instructional Videos' AMNA All Around Dancer (AAD) Classes Dance To Inspire (DTI) Stars www.AMNAdance.com 855-678-AMNA Bollywood | Hip Hop | Jazz | Latin Dance School and Studios Los Angeles County, Orange County and Inland Empire [Most Class Videos are recorded from the mirror View. When practicing, do not reverse any Rights from Lefts. Just follow the video as if it is your mirror] #dancetoinspire #dtistars #amnadance #dancestars
Learn dances step by step: visit AmnaDance.com, click on 'Instructional Videos' AMNA All Around Dancer (AAD) Classes Dance To Inspire (DTI) Stars www.AMNAdance.com 855-678-AMNA Bollywood | Hip Hop | Jazz | Latin Dance School and Studios Los Angeles County, Orange County and Inland Empire [Most Class Videos are recorded from the mirror View. When practicing, do not reverse any Rights from Lefts. Just follow the video as if it is your mirror] #dancetoinspire #dtistars #amnadance #dancestars
Has anyone ever made you feel that you had to tell lies and say bad things about a parent who has always loved and cared for you? You all are welcome to join https://www.facebook.com/groups/MyParentsDivorce/ and tell other kids of divorce! YouTube Channel: Parental Alienation Survival Coach Facebook Group: Parental Alienation Survival Coach Twitter: PASurvivalCoach Instagram: PASurvivalCoach Check out the book! https://www.amazon.com/Parental-Alienation-Survival-Coach-self-care-ebook/dp/B0768SBW7G #parentalalienation #parentalienation
Klee Irwin discusses exceptional lie groups using an analogy of the type of infinite reflections one would see at a barbershop. We interviewed Klee for a documentary we're making about E8 and how different scientists are using it in their quantum gravity theories. This is a mostly unedited portion of his interview.
Made with TextingStory // textingstory.com
Hate Group Falun Dafa Members Organ Harvesting Lie. Hunger Strikes Self-immolations Cults
Hi to everyone! Please watch Bombhaat dance video choreography from the movie Lie starring Nithin and Megha Akash Welcome to Revathi Reddy's dance channel Follow and subscribe if you wish to stay updated. Here is the link https://www.youtube.com/channel/UCUo7T1y-2JYhxBEkQOBcWjw/videos Dance to me is the biggest passion in my life. I love dancing and watching amazing dance videos online. My youtube channel(i.e., Revathi Reddy) is the reflection of my passion towards dance. Every week I would be uploading dance videos from the latest bollywwod and tollywood block buster songs. Please keep on encouraging me and your encourgment boost my confidence levels. You can receive latest updates about my dance videos by liking and following my official dance page on facebook. Here is the link. Pls...
Part 1: https://youtu.be/YvcKrm0FCbI
For more information check out my website: http://freemason90xy.wixsite.com/quantume8
►THE AUDIO IN THIS IS PITCHED DUE TO COPYRIGHT SO PLEASE PLEASE PLEASE CLICK HERE TO WATCH THE ORIGINAL UNPITCHED VERSION!! https://drive.google.com/open?id=0B62h27TleSKoSTBVc0c3Y1RmeXc ■ Song: Hikaru Nara (If It Shines) ■ From: Your Lie in April (Shigatsu wa Kimi no Uso) ■ Composer: Goose-house ■ Instrumental: Also by Goose-House :3 ■ Vocals, Mix, & Master: Cinnabuns [ Here ] -Social: Mixing Commissions: [ https://cinnabuns.wixsite.com/home ] Twitter: [ https://twitter.com/Cinnabunsu ] SoundCloud: [ https://soundcloud.com/major_cinnabuns ] Tumblr: [ http://major-cinnabuns.tumblr.com/ ] ■Illustration and Video: Sketch: Savi [ https://twitter.com/savisavichan ] Lineart: Lilly [ Link below! ] Color: Mina [ https://twitter.com/Minachiio ] Video: Keii [ https://twitter.com/XDkeikoX3 ] ...
Zhiwu Huang; Chengde Wan; Thomas Probst; Luc Van Gool In recent years, skeleton-based action recognition has become a popular 3D classification problem. State-of-the-art methods typically first represent each motion sequence as a high-dimensional trajectory on a Lie group with an additional dynamic time warping, and then shallowly learn favorable Lie group features. In this paper we incorporate the Lie group structure into a deep network architecture to learn more appropriate Lie group features for 3D action recognition. Within the network structure, we design rotation mapping layers to transform the input Lie group features into desirable ones, which are aligned better in the temporal domain. To reduce the high feature dimensionality, the architecture is equipped with rotation pooling la...
Christian pregnancy clinics are suing for the right to lie to their clients. Ana Kasparian and Brett Erlich, the hosts of The Young Turks, break it down. Tell us what you think in the comment section below. https://tytnetwork.com/join/ “Last week Hawaii Gov. David Ige signed a law into effect requiring pregnancy-care centers inform clients about all available reproductive health services, including access to contraception and abortion. Conservative Christian groups are not happy. A day after the law took effect, the Alliance Defending Freedom filed a lawsuit on behalf of A Place for Women in Waipoi, a church-operated crisis pregnancy center, and five other Hawaiian centers affiliated with the National Institute of Family and Life Advocates. They argue that the new law infringes on the ce...
Just Dance Avatar France at Japan Expo (Parc des Expositions, Paris Nord, Villepinte) Category : Group Team : 13 Provence Dance Crew Members : Rayissa, Naf, Yasmiina and Benjamin Song : Hips don't lie Artist : Shakira Ft. Wyclef Jean From Just Dance 2017 #JustDance #Ubisoft #AvatarFrance #JustDancePh #JustDancePhilippines #JustDanceFrance #JustDanceFr #Cosplay #JapanExpo
Abstract: The Hopf algebra of Lie group integrators has been introduced by H. Munthe-Kaas and W. Wright as a tool to handle Runge-Kutta numerical methods on homogeneous spaces. It is spanned by planar rooted forests, possibly decorated. We will describe a canonical surjective Hopf algebra morphism onto the shuffle Hopf algebra which deserves to be called planar arborification. The space of primitive elements is a free post-Lie algebra, which in turn will permit us to describe the corresponding co-arborification process. Joint work with Charles Curry (NTNU Trondheim), Kurusch Ebrahimi-Fard (NTNU) and Hans Z. Munthe-Kaas (Univ. Bergen). The two triangles appearing at 24'04" and 25'19'' respectively should be understood as a #. Recording during the thematic meeting : "Algebraic Combinatorics...
Cooperative SLAM algorithm tested on KITTI dataset.
A representation (character) of a compact Lie group, restricted to the "Kostant principal SU₂" has a weight spectrum which can be interpreted as a sound. Here we listen to the sound thus produced by various representations of various Lie groups (the frequency is set so that the fundamental representation of SU₂ maps to 110Hz, or the A note of the second octave). All compact simple Lie groups up to rank 7 have been included, and for each one, every fundamental representation and the adjoint representation.
At VidUKon 2017, attendees were put into groups and were provided with a range of source material and sections of a song. This is the vid we created. Affectionately known as the Frankenvid, it was screened as the finale of VUK2017.
Double standards and stupid people. Article: https://squawker.org/entertainment-and-gossip/new-study-suggests-rape-culture/
This is from a series of lectures - "Lectures on the Geometric Anatomy of Theoretical Physics" delivered by Dr.Frederic P Schuller
The first in a series of 4 lectures on Lie groups and Lie algebras (with a particular focus on physics) given by Gang Xu, a PSI Fellow, at the 2014-2015 PSI. This lecture provides an introduction to the subject, going through the motivation and basic examples/properties. If you're having trouble seeing the board at any point in the lectures, you can check out this pdf with snapshots of the board -- one shot for each change that occurs: http://pirsa.org/pdf/loadpdf.php?pirsa_number=14080028 These are NOT my videos! All rights, credit, etc. go to the Perimeter Institute, which can be found at the website linked to below. All the videos come from, and can be downloaded from in various formats and from previous years, the Perimeter Institute (where these lectures took place) website: http:...
During the 19th century, group theory shifted from its origins in number theory and the theory of equations to describing symmetry in geometry. In this video we talk about the history of the search for simple groups, the role of symmetry in tesselations, both Euclidean, spherical and hyperbolic, and the introduction of continuous groups, or Lie groups, by Sophus Lie. Along the way we meet briefly many remarkable mathematical objects, such as the Golay code whose symmetries explain partially the Mathieu groups, the exceptional Lie groups discovered by Killing, and some of the other sporadic simple groups, culminating with the Monster group of Fisher and Greiss. The classification of finite simple groups is a high point of 20th century mathematics and the cumulative efforts of many mathe...
Lecture from 2016 upper level undergraduate course in particle physics at Colorado School of Mines
This is the second video in this lecture on simple groups, Lie groups and manifestations of symmetry. During the 19th century, the role of groups shifted from its origin in number theory and the theory of equations to its role in describing symmetry in geometry. In this video we talk about the history of the search for simple groups, the role of symmetry in tesselations, both Euclidean, spherical and hyperbolic, and the introduction of continuous groups, or Lie groups, by Sophus Lie. Along the way we meet briefly many remarkable mathematical objects, such as the Golay code whose symmetries explain partially the Mathieu groups, the exceptional Lie groups discovered by Killing, and some of the other sporadic simple groups, culminating with the Monster group of Fisher and Greiss. The class...
This is from a series of lectures - "Lectures on the Geometric Anatomy of Theoretical Physics" delivered by Dr.Frederic P Schuller
Physicist Carlos Perelman gave a series of lectures on lie algebra to Quantum Gravity Research's team of research scientists. We thought it would be useful for anyone interested in learning more about lie algebra. Quantum Gravity Research is a team of physicists, mathematicians and chemists, hard at work on “Emergence Theory,” a new quantum gravity theory (or “Theory of Everything”) that unifies space, time, energy, matter, information and consciousness. The group was founded by its director, Klee Irwin, and operates in Los Angeles as a non-for-profit organization.
Complete playlist here: https://www.youtube.com/playlist?list=PLMsmpuzEhclYcPYi1wvDuigA41j6-genF
Complete playlist here: https://www.youtube.com/playlist?list=PLMsmpuzEhclYcPYi1wvDuigA41j6-genF
Talk 3 of 4 on Wednesday 05-09-2012
In mathematics, a Lie group is a group that is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure. Lie groups are named after Sophus Lie, who laid the foundations of the theory of continuous transformation groups. The term groupes de Lie first appeared in French in 1893 in the thesis of Lie’s student Arthur Tresse, page 3. Lie groups represent the best-developed theory of continuous symmetry of mathematical objects and structures, which makes them indispensable tools for many parts of contemporary mathematics, as well as for modern theoretical physics. They provide a natural framework for analysing the continuous symmetries of differential equations, in much the same way as permutation groups are used in Galois theory for a...
Complete playlist here: https://www.youtube.com/playlist?list=PLMsmpuzEhclYcPYi1wvDuigA41j6-genF
Introduction to Lie Algebras We will go over the basics of structure and representation theory of finite dimensional complex Lie algebras. We will define basic concepts as ideals, homomorphisms, representations, etc. Then we will move to structure theory of semisimple Lie algebras: Killing form, Casimir elements, root systems, classification of simple algebras. And finally we will go to the basics of representation theory: characters, Weyl formulas, etc. Even though we will try to keep it purely algebraic (1) and we may mention some connections to Lie Group theory and geometry (2). The only previous knowledge that this class will assume is some familiarity with basic algebraic objects like rings and fields. Understanding the notion of manifold would be useful when making connections to Li...
Complete playlist here: https://www.youtube.com/playlist?list=PLMsmpuzEhclYcPYi1wvDuigA41j6-genF
This is from a series of lectures - "Lectures on the Geometric Anatomy of Theoretical Physics" delivered by Dr.Frederic P Schuller
The second in a series of 4 lectures on Lie groups and Lie algebras (with a particular focus on physics) given by Gang Xu, a PSI Fellow, at the 2014-2015 PSI. This lecture covers groups, group representations, structure constants, and the Poincare group. If you're having trouble seeing the board at any point in the lectures, you can check out this pdf with snapshots of the board -- one shot for each change that occurs: http://pirsa.org/pdf/loadpdf.php?pirsa_number=14080029 These are NOT my videos! All rights, credit, etc. go to the Perimeter Institute, which can be found at the website linked to below. All the videos come from, and can be downloaded from in various formats and from previous years, the Perimeter Institute (where these lectures took place) website: http://perimeterschola...
The third in a series of 4 lectures on Lie groups and Lie algebras (with a particular focus on physics) given by Gang Xu, a PSI Fellow, at the 2014-2015 PSI. This lecture discusses the adjoint representation and the highest weight method for constructing representations of su(2). If you're having trouble seeing the board at any point in the lectures, you can check out this pdf with snapshots of the board -- one shot for each change that occurs: http://pirsa.org/pdf/loadpdf.php?pirsa_number=14080030 These are NOT my videos! All rights, credit, etc. go to the Perimeter Institute, which can be found at the website linked to below. All the videos come from, and can be downloaded from in various formats and from previous years, the Perimeter Institute (where these lectures took place) websit...
here is a painfully slow presentation of the first part of Chapter 4 from Erdmann and Wildon. Here we study the derived series of a Lie Algebra which leads us to define the radical as the largest solvable ideal. We conclude by defining semisimple. This is part 1 of 3 (there is about 2 hours of this)
Section 3: invariant vector fields, the exponential map Section 4: the Lie algebra of a Lie group, up to Lemma 4.9 The references (section,corallary,lemma,etc) above are given to 2010 version of lecture notes available at: http://www.staff.science.uu.nl/~ban00101/lie2012/lie2010.pdf The course was given by prof. dr. Erik van den Ban at the University of Utrecht in the spring of 2012 View the complete course ( Exercises, Recommended literature, etc ) at : http://www.staff.science.uu.nl/~ban00101/lie2012/lie2012.html