Comments on: Ado’s theorem
http://terrytao.wordpress.com/2011/05/10/ados-theorem/
Updates on my research and expository papers, discussion of open problems, and other maths-related topics. By Terence TaoFri, 25 Jul 2014 09:55:00 +0000hourly1http://wordpress.com/By: Lie’s Third Theorem and Differential Equations in a Less-Than-Full-Rank Lie Algebra | Wet Savanna Animals
http://terrytao.wordpress.com/2011/05/10/ados-theorem/#comment-396595
Fri, 18 Jul 2014 05:48:21 +0000http://terrytao.wordpress.com/?p=4855#comment-396595[…] Terence Tao, “Ado’s Theorem”; a proof of Ado’s theorem sketched out on Terre… […]
]]>By: Chapter 13: Lie Theoretical Systems Theory | Wet Savanna Animals
http://terrytao.wordpress.com/2011/05/10/ados-theorem/#comment-372234
Mon, 16 Jun 2014 02:48:07 +0000http://terrytao.wordpress.com/?p=4855#comment-372234[…] Terence Tao, “Ado’s Theorem”; a proof of Ado’s theorem sketched out on Terre… […]
]]>By: The Lie Bracket and the Little Adjoint Representation | Wet Savanna Animals
http://terrytao.wordpress.com/2011/05/10/ados-theorem/#comment-277346
Fri, 21 Mar 2014 13:44:01 +0000http://terrytao.wordpress.com/?p=4855#comment-277346[…] Terence Tao, “Ado’s Theorem”; a proof of Ado’s theorem sketched out on Terre… […]
]]>By: The Lie Bracket | Wet Savanna Animals
http://terrytao.wordpress.com/2011/05/10/ados-theorem/#comment-267719
Sun, 26 Jan 2014 06:18:35 +0000http://terrytao.wordpress.com/?p=4855#comment-267719[…] Terence Tao, “Ado’s Theorem”; a proof of Ado’s theorem sketched out on Terre… […]
]]>By: Notes on the classification of complex Lie algebras | What's new
http://terrytao.wordpress.com/2011/05/10/ados-theorem/#comment-226583
Sun, 28 Apr 2013 05:25:10 +0000http://terrytao.wordpress.com/?p=4855#comment-226583[...] to be a homomorphism into a concrete Lie algebra . It is a deep theorem of Ado (discussed in this previous post) that every abstract Lie algebra is in fact isomorphic to a concrete one (or equivalently, that [...]
]]>By: Ado’s theorem for groups with dilations? « chorasimilarity
http://terrytao.wordpress.com/2011/05/10/ados-theorem/#comment-173312
Fri, 21 Sep 2012 11:28:44 +0000http://terrytao.wordpress.com/?p=4855#comment-173312[...] proof I am aware of, (see this post for one proof and relevant links), mixes the following [...]
]]>By: Terence Tao
http://terrytao.wordpress.com/2011/05/10/ados-theorem/#comment-136877
Thu, 05 Apr 2012 15:18:32 +0000http://terrytao.wordpress.com/?p=4855#comment-136877The restriction of the action of on to is simply the original action of on , as can be seen by substituting into (5). The behaviour of becomes irrelevant at that point.
]]>By: Theo
http://terrytao.wordpress.com/2011/05/10/ados-theorem/#comment-136844
Thu, 05 Apr 2012 12:02:09 +0000http://terrytao.wordpress.com/?p=4855#comment-136844Just above Remark 1; why is the enlarged action still faithful on \mathfrak{a}? Couldn’t an element of \mathfrak{h} sit in the centralizer of \mathfrak{a} in \mathfrak{n}?

thanks

]]>By: Associativity of the Baker-Campbell-Hausdorff formula « What’s new
http://terrytao.wordpress.com/2011/05/10/ados-theorem/#comment-98103
Sat, 29 Oct 2011 19:25:31 +0000http://terrytao.wordpress.com/?p=4855#comment-98103[...] With the assistance of Ado’s theorem, which places inside the general linear Lie algebra for some , one can deduce both the well-definedness and associativity of (3) from the Baker-Campbell-Hausdorff formula for . However, Ado’s theorem is rather difficult to prove (see for instance this previous blog post for a proof), and it is natural to ask whether there is a way to establish these facts without Ado’s theorem. [...]
]]>By: 254A, Notes 1: Lie groups, Lie algebras, and the Baker-Campbell-Hausdorff formula « What’s new
http://terrytao.wordpress.com/2011/05/10/ados-theorem/#comment-72425
Fri, 02 Sep 2011 02:15:30 +0000http://terrytao.wordpress.com/?p=4855#comment-72425[...] a global Lie group, requiring the non-trivial algebraic tool of Ado’s theorem (discussed in this previous blog post); see Exercise 20 [...]
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