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$\DeclareMathOperator\SU{SU}$In this question, all Lie algebra cohomology is of the form $H^*(\mathfrak{g}; k)$, with $k$ the trivial one-dimensional representation of $\mathfrak{g}$. All Lie algebra ...

The Schur multipliers of finite simple groups are known and easily accessible: https://en.wikipedia.org/wiki/List_of_finite_simple_groups Moreover, as a consequence of the second Whitehead's Lemma, if ...

Let $L$ be classical Lie algebra of type $A_5$ over field of characteristic 2; let $M$ be the quotient $L/Z(L)$ modulo its center $Z(L)$. What about the group of automorphisms of M? Does anybody ...

I am trying to understand the proof of Theorem 1 from this paper V. Kac and B. Weisfeiler (Indag. Math. 1976, DOI link). Theorem 1. Let either $p\neq 2$ or $\varrho\in X(\mathscr{T})$. Then $\gamma(...

The restriction of an irreducible $\mathfrak{sl}_n(\mathbb{C})$-module to $\mathfrak{sl}_{n-1}(\mathbb{C})$ is described by a branching rule which says that if $L(\lambda)$ is the simple $\mathfrak{sl}...

Let $L$ be a Lie algebra over a field of characteristic $p>0$ and $D$ a derivation of $L$. For every $x\in L$ denote by $\mathrm{ad} x$ the adjoint map $\mathrm{ad}x: L \rightarrow L, a\mapsto [x,...