Let’s start with subalgebra A⊂GL(N,R)A \subset GL(N, R) with commutator as Lie bracket. It has subset of invertable elements which form group GG.
I want to proof (if it’s true of course)
GG is Lie group
Lie algebra of GG is AA
I don’t understand this question. Lie algebras don’t have invertible elements, as x^2 = 0 for all elements x. However, if you mean in the underlying associative algebra, then every element is invertible.
– David Towers
13 hours ago