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Linear representations of algebras and groups, Lie theory, associative algebras, multilinear algebra.

2 votes
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629 views

When is there a $g$-module isomorphism between a semi-simple Lie algebra $g$ and an exterior...

Let $g$ be a semi-simple Lie algebra, and $0 \to I \to h \to g \to 0$ an Abelian extension of $g$. Then $g$ acts on $I$. Considering $g$ under the adjoint action, when is there a $g$-module isomorph …