Questions tagged [modular-lie-algebras]

Lie algebras in positive characteristic (not necessarily restricted Lie algebras)

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14
votes
3answers
2k views

Which is the correct universal enveloping algebra in positive characteristic?

This is an extension of this question about symmetric algebras in positive characteristic. The title is also a bit tongue-in-cheek, as I am sure that there are multiple "correct" answers. Let $\...
8
votes
3answers
958 views

Failure of Jacobson-Morozov in positive characteristics

The Jacobson-Morozov theorem that any nilpotent element $e$ in the Lie algebra of a simple algebraic group $G$ can be embedded in an $\mathfrak{sl}_2$-triple, has a restriction (in terms of the ...
4
votes
2answers
604 views

Lie's theorem in characteristic $p$

Let $K$ be an algebraically closed field with characteristic $0$ and $V$ be a Lie sub-algebra of $M_n(K)$, the $n\times n$ matrices over $K$. If $V$ is solvable, then, according to Lie's theorem, $V$ ...