# Questions tagged [modular-lie-algebras]

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

3
questions

**14**

votes

**3**answers

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

**3**answers

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

**2**answers

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, $V$ ...