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I have seen two constructions called the Heisenberg group. If $k$ is a field of characteristic not equal to $2$ and $V$ is a $2n$-dimensional vector space over $k$ with symplectic form $\omega : V \...

Let $1\to H\to E\to G\to 1$ be a short exact sequence of algebraic groups defined over an algebraically closed field $k$ of characteristic $p$. Suppose $H$ is a finite group, and $G$ and $E$ are ...

Let $k$ be a field; I'm going to discuss linear algebraic groups over $k$. The question I'll pose is only interesting when the characteristic is $p>0$. 1. Some motivation A vector group is an ...

Classical theorems attributed to Levi, Mal'cev, Harish-Chandra for a finite dimensional Lie algebra over a field of characteristic 0 state that it has a Levi decomposition (semisimple subalgebra plus ...