Dear @fresh_42 , Hope you are well.
Please, I have a question if you do not mind, about Lie Algebra,
In page 2 in the book of Lie algebra, written by Humphreys,
Classical Lie algebras, ##A, B, C## and ##D##, I did not get it well, especially, symplectic and orthogonal..
Could you please...
Thank you so much, @fresh_42 , please, why Universal enveloping algebra is module? PBW theorem gives a basis of Universal enveloping algebra, but please, why it is finite dimensional? please,
I thougt in general: lie lagebra is finite dimensioal, and its universal enveloping is infinite...
Please, I have a question about this:
The Universal enveloping algebra of a finite dimensional Lie algebra is Noetherian.
How we can prove it? Please..
Dear, @fresh_42 , I am so sorry, but I have a question here:
about: (b), I need example of it, and I found: upper triangular matrix, let it ##A##, so if we bracket ##A## with itself, we will get strictly upper matrix, which is nilpotent, and then: solvable ideal, but what about the quotient of...
Please, @fresh_42 , in theorem 5.2 page: 23, about semi simple:
how we apply Cartan criterian on ##I \cap I^{\perp}##,
Thank you very much, :heart: :heart:
Please, I have a question about automorphism:
Let ##\mathbb{K}## be a field, if ##\operatorname{char}(\mathbb{K})=p ##, then the order of automorphism ##\phi## is ##p##, i.e. ##\phi^p=\operatorname{id}##, where ##i d## is identity map.
Is that right? please, if yes, how we can prove it, and...
Please, @fresh_42 , bear with me, here what will be the equivalncve classes of ##\mathfrak{g l}(2) / \mathfrak{s l}(2) \cong \mathbb{K}##?
I mean as in ##{0+3Z,1+3Z, 2+3Z}## in ##\mathbb{Z}_3##.
Thank in advance, :heart:
Please, I have a question about Schur's Lemma ;
Let $\phi: L \rightarrow g I((V)$ be irreducible. Then the only endomorphisms of $V$ commuting with all $\phi(x)(x \in L)$ are the scalars.
Could you explain it, and please, how we can apply this lemma on lie algebra ##L=\mathfrak{s l}(2)##thanks...
Thank you so much, @fresh_42 , please, do you know how we get this element?
I mean this form: ##\frac{1}{2} H^2+H+2 F E##
I found it in page 28.
Thanks in advance, :heart: :heart: