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Results tagged with rt.representation-theory
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user 14312
Linear representations of algebras and groups, Lie theory, associative algebras, multilinear algebra.
7
votes
2
answers
2k
views
When is the Levi subalgebra an ideal?
Let $L$ be a Lie algebra. It is known that $L$ admits a Levi decomposition (possibly non unique):
$L=S\oplus rad(L) $,
where $rad(L)$ is the solvable radical and $S$ is a semisimple subalgebra.
If …
- 52.9k
10
votes
2
answers
1k
views
Abstract Jordan Decomposition different from usual Jordan Decomposition
It's known that if $L\subset gl(V)$, with $V$ finite dimensional, is a semisimple Lie algebra, then the abstract and usual Jordan decompositions in $L$ coincide. Is it possible to provide a counter-ex …
- 19.6k
5
votes
2
answers
315
views
Radical of projection equals projection of radical?
Given an Lie Algebra $L$ (of finite dimension and over an algebraically closed field with zero characteristic) and an ideal $I$, is it truth that
$rad\left(\dfrac{L}{I}\right)= \pi(rad(L))$,
where …
- 349