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Bookmark or Share- Toral subalgebra of a semisimple Lie algebra is abelian.The intersection of a maximal toral subalgebra with a simple ideal of a Lie algebra is a maximal toral subalgebra of the simple ideal. 1 Proof that a semisimple Lie algebra can be written as sum of two ideals
- terminology - Where does the name "toral" come from? - Mathematics ...$\begingroup$ Toral subalgebras (of a Lie algebra) are those in which every element is diagonalizable. Is this condition equivalent to being the Lie algebra of a torus? I'm not interested in the etymology of the word "torus," but rather in the connection between toral subalgebras (as defined here) and tori. $\endgroup$ –
- lie algebras - Abelian subalgebra doesn't imply toral - Mathematics ...Now, every toral subalgebra is abelian. But, what is an example for an abelian subalgebra which is not toral?
- reference request - expansive toral automorphism and forward expansive ...$\begingroup$ Probably the best reference for this subject is Schmidt's book - dynamical system of algebraic origins, where he characterizes toral automorphisms (and more) by algebraic methods. I guess this claim should appear in Rudolph's book, but I'm not 100% sure about that. $\endgroup$
- lie algebras - Commuting matrices and centralizer of a maximal toral ...Any nontrivial semisimple Lie algebra has infinitely many such CSA's a.k.a. maximal toral subalgebras. Next, the quoted fact that the subalgebra of all diagonal matrices forms a (not "the") CSA a.k.a. maximal toral subalgebra in the full matrix algebra $\mathfrak{gl}_n$ is very good to know, but falls short of relevance here.
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