Lie theory (pronounced "Lee") is an area of mathematics, developed initially by Sophus Lie.

In Lie's early work, the idea was to construct a theory of continuous groups, to complement the theory of discrete groups that had developed in the theory of modular forms, in the hands of Felix Klein and Henri Poincaré. The initial application that Lie had in mind was to the theory of differential equations. On the model of Galois theory and polynomial equations, the driving conception was of a theory capable of unifying, by the study of symmetry, the whole area of ordinary differential equations.

The hope that Lie Theory would unify the entire field of ordinary differential equations was not fulfilled. Symmetry methods for ODEs continue to be studied, but do not dominate the subject. There is a differential Galois theory, but it was developed by others, such as Picard and Vessiot, and it provides a theory of quadratures, the indefinite integrals required to express solutions.

In the longer term, it has not been the direct application of continuous symmetry to geometric questions that has made Lie theory a central chapter of contemporary mathematics. The fact that there is a good structure theory for Lie groups and their representations has made them integral to large parts of abstract algebra. Some major areas of application have been found, for example in automorphic representations and in mathematical physics, and the subject has become a busy crossroads.

Elementary Lie theory

The one-parameter groups are the first instance of Lie theory. The compact case arises through Euler's formula in the complex plane. Other one-parameter groups occur in the split-complex number plane as the hyperbola :$\backslash exp(j\; t)\; =\; \backslash cosh(t)\; +\; j\; \backslash sinh(t)\; \backslash quad\; t\; \backslash in\; R\; ,$ and in the dual number plane as the line $\backslash exp(\backslash epsilon\; t)\; =\; 1\; +\; \backslash epsilon\; t\; \backslash quad\; t\; \backslash in\; R.$ In these cases the Lie algebra parameters have names: angle, hyperbolic angle, and slope. Using the appropriate "angle", and a radial vector, any one of these planes can be given a polar decomposition. Any one of these decompositions, or Lie algebra renderings, may be necessary for rendering the Lie subalgebra of a 2 × 2 real matrix.

There is a classical 3-parameter Lie group and algebra pair: the quaternions of unit length which can be identified with the 3-sphere. Its Lie algebra is the subspace of quaternion vectors. Since the commutator ij − ji = 2k, the Lie bracket in this algebra is twice the cross product of ordinary vector analysis.

Aspects of Lie theory

The foundation of Lie theory is the exponential map relating Lie algebra to Lie group. Structure is captured in Root systems and root data. Lie theory is frequently built upon a study of the classical linear algebraic groups. Special branches include Weyl groups, Coxeter groups, and buildings. The classical subject has been extended to Groups of Lie type.

In 1900 David Hilbert challenged Lie theorists with his Fifth Problem presented at the International Congress of Mathematicians in Paris.

See also

List of Lie group topics

References

Thomas Hawkins (2000) Emergence of the Theory of Lie Groups: an essay in the history of mathematics, 1869 — 1926, Springer ISBN 0387989633 .

David H. Sattinger & O.L. Weaver (1986) Lie groups and algebras with applications to physics, geometry, and mechanics Springer-Verlag ISBN 3540962409 .

John Stillwell (2008) Naive Lie Theory, Springer ISBN 0387982892.

Category:Lie groups Category:Differential equations Category:History of mathematics

Name	Jesse Ventura
Order	38th
Office	Governor of Minnesota
Term start	January 8, 1999
Term end	January 6, 2003
Lieutenant	Mae Schunk
Predecessor	Arne Carlson
Successor	Tim Pawlenty
Office2	Mayor of Brooklyn Park, Minnesota
Term start2	1991
Term end2	1995
Birthname	James George Janos
Birth date	July 15, 1951
Birth place	Minneapolis, Minnesota
Spouse	Terry Ventura
Children	Tyrel Ventura Jade Ventura
Profession	US Navy UDT Professional Wrestler Color commentator Actor Talk Show host Politician Author
Party	Reform Party (1999–2000) Independence Party of Minnesota (2000–present)
Branch	United States Navy
Serviceyears	1969–1975
Rank	Petty Officer
Unit	Underwater Demolition Team 12 United States Navy
Awards	National Defense Service Medal Vietnam Service Medal

James George Janos (born July 15, 1951), better known as Jesse Ventura, is an American politician, the 38th Governor of Minnesota from 1999 to 2003, Navy UDT veteran, actor, and former radio and television talk show host. As a professional wrestler, he is best known for his nickname, Jesse "The Body" Ventura, and tenure in the World Wrestling Federation as a combatant and color commentator. In 2004, he was inducted into the company's Hall of Fame. Ventura has described himself as Slovak. Ventura (then still using his legal name of Janos) attended the now-closed Cooper Elementary School and graduated from Minneapolis' Roosevelt High School in 1969.

Navy career

From September 11, 1969, to September 10, 1975, during the Vietnam War era, Ventura served in the United States Navy. While on active duty, Ventura was part of Underwater Demolition Team 12 (UDT). The UDTs were merged with the US Navy SEALs in 1983, 8 years after Ventura had left the Navy.

Bill Salisbury, an attorney in San Diego and a former Navy SEAL officer, accused Ventura of "pretending" to be a SEAL and wrote that Ventura would be blurring an important distinction by claiming to be a SEAL when he was actually a frogman with the UDT. Compared to SEAL teams, UDTs saw less combat and took fewer casualties. Following that, Governor Ventura's office confirmed that Ventura was never a member of the SEALs. His spokesman stated that Ventura has never tried to convince people otherwise. He was criticized by hunters and conservationists for stating in an interview with the Minneapolis StarTribune in April 2001, "Until you have hunted men, you haven't hunted yet."

In January 2002, Ventura, who had never specifically claimed to have fought in Vietnam, disclosed for the first time that he did not see combat. He did not receive the Combat Action Ribbon, which was awarded to those involved in a firefight or who went on clandestine or special operations where the risk of enemy fire was great or expected.

In the fall of 1974, Ventura left the bike club to return to Minnesota. Shortly after leaving, the Mongols entered into open warfare with their rivals the Hells Angels.

Professional wrestling career

Name	Jesse Ventura
Names	Jesse "The Body" Ventura Years later, as a broadcaster, Ventura made a running joke out of claiming that Graham stole all of his ring attire ideas from him.
Show name	Jesse Ventura's America
Caption	Ventura on his MSNBC talk show Jesse Ventura's America
Starring	Jesse Ventura
Location	Saint Paul, Minnesota,
Network	MSNBC
First aired	October 4, 2003
Last aired	December 26, 2003
Italic title	no

Ventura was succeeded in his office by Republican Tim Pawlenty. He began a cable television show in October 2003, on MSNBC called Jesse Ventura's America. The show was broadcast once a week, on Saturdays, unlike many MSNBC shows which are on five nights a week (this show was originally planned for five nights a week as well, but MSNBC executives changed their minds). At the time of its airing, Jesse Ventura's America was the only national television show filmed in Minnesota. Among his guests were Charles Barkley, Gray Davis, Arianna Huffington, Rob Kampia, and Kathy McKee.

In 2004, fellow Navy veteran and Harvard graduate student Christopher Mora promoted the idea that the academic establishment had failed to reach out to citizens experienced in public service, but who did not fit the traditional idea of a politician. He successfully lobbied for the selection of Ventura, who started teaching a study group at Harvard University for the Spring 2004 semester as a visiting fellow at the Kennedy School of Government's Institute of Politics (IOP). His 90-minute study group focused on third party politics, campaign finance, the war on drugs, and other relevant political issues. Ventura scheduled multiple famous friends to appear for his seminars including Dean Barkley and Richard Marcinko.

On October 22, 2004, with Ventura by his side, former Maine Governor Angus King endorsed John Kerry for President at the Minnesota state capitol building. Ventura did not speak at the press conference. When prodded for a statement, Governor King responded, "He plans to vote for John Kerry, but he doesn't want to make a statement and subject himself to the tender mercies of the Minnesota press".

In November 2004, an advertisement began airing in California featuring Ventura. In it, Ventura voices his opposition to Governor Arnold Schwarzenegger's policies regarding Native American casinos. Like Hogan, Schwarzenegger at one point was also a close friend of Ventura as well, but since Schwarzenegger's victory in California, Ventura has not reportedly given him any praise; Schwarzenegger didn't even mention Ventura's name in an interview with Fox News in 2005, where reporter Chris Wallace asked him if he was "the next Jesse Ventura". Ventura is serving as an advisory board member for a new group called Operation Truth, a non-profit organization set up "to give voice to troops who served in Iraq." “The current use of the National Guard is wrong....These are men who did not sign up to go occupy foreign nations”.

In August 2005, Ventura became the spokesperson for BetUS, an online Sportsbook. In 2005, Ventura repeatedly discussed leaving the United States. In September 2005, Ventura announced on The Mike Malloy Show that he was leaving the U.S. and planned to "have an adventure". In late October 2005, he went on The Big Idea with Donny Deutsch and reiterated that he was leaving the U.S. due to, among other things, censorship. He has since moved to Baja California, Mexico.

In September 2006, Ventura endorsed and campaigned with independent Texas gubernatorial candidate Kinky Friedman, and Independence Party of Minnesota's gubernatorial candidate Peter Hutchinson and Team Minnesota. He revealed he now spends much of his time surfing near his home in Mexico.

In April 2008, a book authored by Ventura, titled Don't Start the Revolution Without Me, was released. In it, Ventura describes a hypothetical campaign in which he is a candidate for President of the United States in 2008, running as an independent. In an interview with the Associated Press at the time of the book's release, however, Ventura denied any plans for a presidential bid, stating that the scenario is only imaginary and not indicative of a "secret plan to run". On MinnPost.com, Ventura's agent, Steve Schwartz, describes the book thus: "[Ventura is revealing] why he left politics and discussing the disastrous war in Iraq, why he sees our two-party system as corrupt, and what Fidel Castro told him about who was really behind the assassination of President Kennedy."

However, in an interview on CNN's The Situation Room on April 7, Ventura hinted that he was considering entering the race for the United States Senate seat then held by Norm Coleman, his Republican opponent in the 1998 Gubernatorial race. A poll commissioned by Twin Cities station Fox 9 put him at 24 percent, behind Al Franken at 32 percent and Norm Coleman at 39 percent in a hypothetical three-way race. However, Ventura announced on Larry King Live on July 14, 2008 that he would not run.

He spoke at former Republican presidential candidate Ron Paul's "Rally for the Republic", organized by the Campaign for Liberty, on September 2, 2008. At the event, Ventura implied a possible future run at the U.S. Presidency. Ventura stated before a live audience that "If America proves itself worthy, in 2012 we'll give them a race they'll never forget!"

TV Week is reporting that Ventura is in negotiations with 20th Television to host a half-hour court show that would debut in the fall of 2009.

Bush/Cheney administration and torture

In a May 11, 2009 interview with Larry King, Ventura twice stated that George W. Bush was the worst president of his lifetime, adding "President Obama inherited something I wouldn't wish on my worst enemy. You know? Two wars, an economy that's borderline depression." On the issue of waterboarding, Ventura added:

I'll put it to you this way, you give me a water board, Dick Cheney and one hour, and I'll have him confess to the Sharon Tate murders. ... If it's done wrong, you certainly could drown. You could swallow your tongue. [It] could do a whole bunch of stuff to you. If it's done wrong orit's torture, Larry. It's torture. Ventura also expressed interest in being appointed ambassador to Cuba should U.S. relations with Cuba continue to improve. On a May 18, 2009 appearance on The View, Ventura asked Elisabeth Hasselbeck if waterboarding is acceptable, why were not Oklahoma City bombers, Timothy McVeigh and Terry Nichols waterboarded. "We only seem to waterboard Muslims." Comparing the waterboarding of detainees to the North Vietnamese torture of American P.O.W.s, Ventura asserted, "We created our own Hanoi Hilton in Guantánamo. That's our Hanoi Hilton."

Questions regarding 9/11

In April and May 2008, Jesse Ventura, in several radio interviews for his new book, Don't Start the Revolution Without Me, expressed concerns about what he described as some of the unanswered questions of the September 11 attacks. His remarks about the possibility that the World Trade Center was demolished with explosives were also repeated in newspaper and television stories following some of the interviews.

Ventura was interviewed on the Alex Jones radio show on April 2, 2008 where he said that he felt that many unanswered questions remain, and he believes that World Trade Center Building 7, which was not struck by a plane, collapsed on the afternoon of 9/11 in a manner which resembled a controlled demolition Ventura stated:

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He also states the Twin Towers appeared to be pulverized to dust, that they fell at virtually free-fall speed, and that no other massive steel-framed buildings had ever collapsed in this manner due to fire before.

Conspiracy Theory with Jesse Ventura

In August 2009, it was announced that Ventura would host TruTV's new show Conspiracy Theory with Jesse Ventura. "Ventura will hunt down answers, plunging viewers into a world of secret meetings, midnight surveillance, shifty characters and dark forces," truTV said in a statement. On the program, which debuted on December 2, 2009, Ventura travels the country, investigating cases and getting input from believers and skeptics before passing judgment on a theory's validity. According to TruTV, the first episode drew 1.6 million viewers, a record for a new series on the network.

American Conspiracies

American Conspiracies is a book Ventura wrote with Dick Russell, published by Skyhorse Publishing in 2010 which discusses conspiracy theories related to several notable events in United States history.

Personal life

In 1975, Ventura married his wife Terry. The couple have two grown children: a son, Tyrel (b. 1980), who is a movie and television director and producer, and a daughter, Jade (b. 1983).

During his wrestling days, Ventura used anabolic steroids. He admitted this after retiring from competition, and went on to make public service announcements and appear in printed ads and on posters warning young people about the potential dangers and potential health risks of abusing steroids.

In 2002, Ventura was hospitalized for a severe blood clot in his lungs, the same kind of injury that ended his wrestling career.

Currently, Ventura and his wife live in Mexico, "There are no newspapers down where I live. Where I live, I'm an hour from pavement and an hour from electricity..I'm completely off the grid."

Religion

In a Playboy interview, he said, "Organized religion is a sham and a crutch for weak-minded people who need strength in numbers. It tells people to go out and stick their noses in other people's business." In his 1999 best-selling memoir I Ain't Got Time to Bleed, Ventura responded to the controversy sparked by these remarks by elaborating on his views concerning religion: "I’d like to clarify [my comments published in Playboy] about religious people being weak-minded. I didn’t mean all religious people. I don’t have any problem with the vast majority of religious folks. I count myself among them, more or less. But I believe because it makes sense to me, not because I think it can be proven. There are lots of people out there who think they know the truth about God and religion, but does anybody really know for sure? That’s why the founding fathers built freedom of religious belief into the structure of this nation, so that everybody could make up their minds for themselves. But I do have a problem with the people who think they have some right to try to impose their beliefs on others. I hate what the fundamentalist fanatics are doing to our country. It seems as though, if everybody doesn’t accept their version of reality, that somehow invalidates it for them. Everybody must believe the same things they do. That’s what I find weak and destructive."

Ventura endorsed equal rights for religious minorities, as well as people who don't believe in God, by declaring July 4, 2002, "Indivisible Day". Ventura proclaimed October 13–19, 2002 as "Christian Heritage Week" in Minnesota.

In 2010, regarding the Ground Zero Mosque controversy, Ventura argued, "Excuse me, the Constitution says they can do it, it ends there! You cannot subject the Constitution to a popularity poll," in reference to the opposition of the mosque. In a separate interview on CNN, when told that the victims' families needed to be respected, Ventura replied, "But what's the problem? I mean, Timothy McVeigh, I assume, was a Christian and he did an act of terrorism. Would they then remove all Christian churches from around Oklahoma City, because it happened to have been a Christian that did it? You know, it's ridiculous."

Electoral history

1998 election for Governor

*Jesse Ventura (Ref.), 37%

*Norm Coleman (R), 34%

*Hubert H. Humphrey III (DFL), 28%

Books

I Ain't Got Time to Bleed: Reworking the Body Politic from the Bottom Up ISBN 978-0-451-20086-0

Do I Stand Alone?: Going to the Mat Against Political Pawns and Media Jackals ISBN 978-0-7434-0587-4

Jesse Ventura Tells It Like It Is: America's Most Outspoken Governor Speaks Out About Government (co-authored with Heron Marquez) ISBN 978-0-8225-0385-9

Don't Start the Revolution Without Me! (co-authored with Dick Russell) ISBN 978-1-60239-273-1

American Conspiracies (March 2010, co-authored with Dick Russell) ISBN 978-1602398023

Notes

References

deFiebre, Conrad. "Record-high job approval for Ventura; Many Minnesotans like his style, don't mind moonlighting." Star Tribune 22 July 1999: 1A+.

deFiebre, Conrad. "Using body language, Ventura backs Kerry." Star Tribune 23 October 2004: 1A+.

Kahn, Joseph P. "The Body Politic." The Boston Globe 25 February 2004. Accessed April 28, 2004.

Olson, Rochelle and Bob von Sternberg. "GOP demands equal time; Wellstone aide apologizes; Ventura upset." Minneapolis Star-Tribune 31 October 2002: 1A+.

External links

WWE Hall of Fame Profile

Ventura "on the issues"

Analysis of Jesse Ventura's Playboy interview by Aubrey Immelman

Jesse Ventura – Media Man Australia profile

Election Of Bonapartist Figure Ventura In Minnesota Is Danger To Working People – article in The Militant 1998.

Radiotapes.com Recordings of Jesse Ventura for Governor commercials from 1998 (scroll down to Misc Recordings).

Larry King Live: Jesse Ventura CNN April 1, 2008

"Jesse's back! New Ventura book 'Revolution' will cover political waterfront" from Minnpost.com

The Jesse Ventura Forums

Jesse Ventura on Wrestling-Radio.com

Jesse Ventura interview, Diaday.com

Jesse Ventura on The Young Turks Show.

Category:Actors from Minnesota Category:American actor-politicians Category:American athlete-politicians Category:American film actors Category:American memoirists Category:American military personnel of the Vietnam War Category:American professional wrestlers Category:American talk radio hosts Category:American television sports announcers Category:American actors of German descent Category:American sportspeople of German descent Category:Governors of Minnesota Category:Mayors of places in Minnesota Category:Mongols (motorcycle club) Category:Radio personalities from Minneapolis, Minnesota Category:Professional wrestling announcers Category:Reform Party of the United States of America politicians Category:Minnesota Vikings broadcasters Category:Tampa Bay Buccaneers broadcasters Category:United States Navy sailors Category:WWE Hall of Fame Category:1951 births Category:Living people Category:Independence Party of Minnesota politicians Category:American sportspeople of Slovak descent Category:American politicians of Slovak descent Category:American actors of Slovak descent