Timeline for Lie algebras with abelian Cartan subalgebras

6 events

when toggle format	what		by	license	comment
Feb 18, 2012 at 18:54	comment	added	B R		But an abelian Lie algebra is reductive!
Feb 18, 2012 at 18:52	comment	added	anon		Even simpler, an abelian Lie algebra is a Cartan subalgebra of itself.
Feb 18, 2012 at 16:46	comment	added	Salvatore Siciliano		BR: Yes, you are right.
Feb 18, 2012 at 16:32	comment	added	B R		This method works whenever $\mathfrak b$ is a subalgebra of a reductive Lie algebra $\mathfrak g$ and $\mathfrak b$ contains a Cartan subalgebra $\mathfrak a$ of $\mathfrak g$ (Since $\mathfrak a$ is its own normalizer in $\mathfrak g$, it will be its own normalizer in $\mathfrak b$).
Feb 18, 2012 at 16:27	comment	added	Salvatore Siciliano		Indeed, the subalgebra of diagonal matrices is also a Cartan subalgebra of $gl_n(F)$ for any field $F$ and $n>0$.
Feb 18, 2012 at 4:59	history	answered	B R	CC BY-SA 3.0