- published: 30 Jan 2017
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In abstract algebra, Ado's theorem is a theorem characterizing finite-dimensional Lie algebras.
Ado's theorem states that every finite-dimensional Lie algebra L over a field K of characteristic zero can be viewed as a Lie algebra of square matrices under the commutator bracket. More precisely, the theorem states that L has a linear representation ρ over K, on a finite-dimensional vector space V, that is a faithful representation, making L isomorphic to a subalgebra of the endomorphisms of V.
It was proved in 1935 by Igor Dmitrievich Ado of Kazan State University, a student of Nikolai Chebotaryov.
The restriction on the characteristic was removed later, by Iwasawa and Harish-Chandra (see also the below Gerhard Hochschild paper for a proof).
While for the Lie algebras associated to classical groups there is nothing new in this, the general case is a deeper result. Applied to the real Lie algebra of a Lie group G, it does not imply that G has a faithful linear representation (which is not true in general), but rather that G always has a linear representation that is a local isomorphism with a linear group.
Paul Horowitz (born 1942) is an American physicist and electrical engineer, known primarily for his work in electronics design, as well as for his role in the search for extraterrestrial intelligence (see SETI).
At age 8, Horowitz achieved distinction as the world's youngest amateur radio operator (or "ham"). He went on to study physics at Harvard University (B.A., 1965; M.A., 1967; Ph.D., 1970), where he has also spent all of his subsequent career. His early work was on scanning microscopy (using both protons and X-rays). Horowitz has also conducted astrophysical research on pulsars and investigations in biophysics. His interest in practical electronics has led to a handful of inventions, including an automated voting machine and an acoustic mechanism for landmine detection. Since 1974 he has taught a practical course in electronics whose lecture notes became one of the best known textbooks in the field: The Art of Electronics (coauthored with Winfield Hill).
Horowitz was one of the pioneers of the search of intelligent life beyond the Earth, and one of the leaders behind SETI. This work has attracted both admiration and criticism. Harvard biologist Ernst Mayr has sharply criticized Horowitz for wasting the resources of the university and the efforts of graduate students on such an endeavour. Carl Sagan provided a strong rebuttal to Mayr's criticism, and pointed out that many eminent biologists and biochemists had endorsed SETI with the statement:
Big Brother has spotted some rule breaking, and there's a punishment in store for a couple of naughty housemates...
No cats were harmed in the making of this video. Tweet it - http://bit.ly/qJZry7 Facebook it - http://on.fb.me/rfgo9J minutephysics is now on Google+ - http://bit.ly/qzEwc6 And facebook - http://facebook.com/minutephysics Minute Physics provides an energetic and entertaining view of old and new problems in physics -- all in a minute! In this episode we discuss Schrödinger's cat, quantum entanglement, and our perception of reality. Music by Nathaniel Schroeder youtube: http://bit.ly/pakJLE myspace: http://mysp.ac/qtmZQj German translation by http://www.youtube.com/user/TesaFilmEnt?feature=watch Created by Henry Reich Created by Henry Reich
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Gravity, Pendulums and the Conservation of Energy - Lecture 1 - June 25, 2012.
World-renowned neuroscientist, entrepreneur, and two-time TED speaker Beau Lotto draws on over two decades of research to reveal startling truths about the brain and how it perceives the world. In DEVIATE, Beau answers the long-debated question: do humans see reality or not? Spoiler alert: we don't. In fact, our brains didn’t – couldn’t! – evolve to see the world accurately. What we see is subjective, not objective. This fundamental revelation shows that everything we know is filtered by each individual's past experiences. It’s the reason why “dressgate” confounded the world and broke the internet in 2015. Explore that and more in DEVIATE. Get the book here: https://goo.gl/Iqp20W
Subscribe to TRAILERS: http://bit.ly/sxaw6h Subscribe to COMING SOON: http://bit.ly/H2vZUn Like us on FACEBOOK: http://goo.gl/dHs73 Follow us on TWITTER: http://bit.ly/1ghOWmt Sharknado 2: The Second One Official Trailer #1 (2014) - Syfy Channel Sequel HD A freak weather system turns its deadly fury on New York City, unleashing a Sharknado on the population and its most cherished, iconic sites - and only Fin and April can save the Big Apple. The Movieclips Trailers channel is your destination for the hottest new trailers the second they drop. Whether it's the latest studio release, an indie horror flick, an evocative documentary, or that new RomCom you've been waiting for, the Movieclips team is here day and night to make sure all the best new movie trailers are here for you the moment ...
Veteran investigative journalist John Bloom tells the greatest satellite story you've never heard, with special guests Dr. Ray Leopold and Dan Colussy. The Iridium satellite constellation--dreamed up by Dr. Ray Leopold and co. in the '90s--was intended to provide a cellular phone with signal at all ends of the Earth. As the dotcom bubble burst, and Motorola struggled to find buyers for its $5 billion project, the Iridium project was almost self-destructed out of orbit. But businessman Dan Colussy had other plans.
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Is it possible to build a lightsaber made out of light? Figuring out how to go about building a lightsaber gives us the perfect excuse to learn about new exotic states of light and matter at the cutting edge of science and technology. Are you ready? Let's dive in! ** Please support my channel by becoming a patron: http://www.patreon.com/crackingthenutshell ** Or... how about a Paypal Donation? http://crackingthenutshell.org/donate Full script here: http://crackingthenutshell.org/the-physics-of-lightsabers-stopping-light-photonic-molecules-bose-einstein-condensates Have you ever wondered if it’s possible to build a real-life lightsaber? And if so, would it be possible to make it out of light (as opposed to using plasma instead)? I mean, after all, we want to make a lightsaber not a pla...
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Converse of a Perpendicular Theorem - Theorem on Circles CBSE Class IX ICSE Class X - Theorem 2 - In a circle a line drawn from centre of a circle bisecting a chord is always perpendicular to the chord by Ankit Mahajan for SuccessCDs Education Channel. For all Maths lessons , please visit http://goo.gl/RauMr SuccessCDs Education ( http://www.youtube.com/successcds1 ) is an online education channel focused on providing education through Videos as per CBSE, ICSE and NCERT syllabi upto Class 12 (K-12) for English, Maths, Hindi, Science,Social Science, Sanskrit and other subjects. Also visit our Channel for Entrance Exams in India FAQs & Application Process, GK & Current Affairs, Communication Skills Our website ( http://www.successcds.net ) is one of the leading portal on Entrance Exam...
Paul Horowitz visited Google's office in Cambridge, MA to discuss the SETI (Search for Extraterrestrial Intelligence) project at Harvard University. Establishing an electromagnetic communications link across a thousand light-years presents unique technological challenges. In his talk, Prof. Horowitz visits some highlights of the science and technology of SETI -- Do THEY exist? Is communication possible? What is the best way? Is this just completely insane? -- and describes interesting searches his project and others have been doing. Paul Horowitz is a Research Professor of Physics and of Electrical Engineering at Harvard, and is co-author of The Art of Electronics. SETI at Harvard was supported in part by grants from NASA, The Planetary Society, and the Bosack/Kruger Charitable Fou...
Available on VOD: January 7, 2014 In Theaters: January 31, 2014 In the role of Royal Marine, A.J. Budd, Joseph Morgan stars in this brutal psychological and supernatural thriller, in which he finds himself trapped in the Warhouse. Imprisoned, he is forced to fight for his life against grotesque, inhuman opponents. He must kill every day or die himself. His one glimmer of hope comes in the form of a diary, left by a former occupant of the house, WWI Lieutenant Edward Sterling, played by Matt Ryan.
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