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3 votes
1 answer
279 views

Wedderburn–Artin like theorem for infinite dimensional Lie algebras?

The Wedderburn–Artin Theorem is one of the cornerstones of the structure theory of (associative) rings. Wedderburn–Artin Theorem : Let $R$ be a left Artinian ring with zero Jacobson radical. Then $R$ ...
5 votes
0 answers
142 views

Is there a notion of octonionic structure on a Lie algebra? In the same way as there is one for complex and quaternionic

Is there a notion of octonionic structure on a Lie group? In the same way as there is one for complex and quaternionic
11 votes
1 answer
312 views

Homotopes of simple Lie algebras

Let $\mathfrak{g}$ be a complex simple Lie algebra with bracket $[x,y]$. For which $z\in \mathfrak{g}$ does the formula $$ \mu(x,y)=ad (z)([x,y])=[z,[x,y]] $$ define another Lie bracket on the same ...