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3 votes
1 answer
126 views

Schur multiplier of finite-dimensional simple Lie algebras in positive characteristic

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 …
Rocky Smith's user avatar
11 votes
1 answer
333 views

An identity in Lie algebras over fields of positive characteristic

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 $\mathrm{ad}x: L \rightarrow L, a\mapsto [x,a]$ …
Rocky Smith's user avatar
4 votes
1 answer
128 views

Second cohomology group of the contact Lie algebra $K_3$

Let $F$ be a field of characteristic zero and, for all $n>0$, consider the contact Lie algebra $K_{2n+1}$. It follows from Corollary 3 of the paper [V. Guillemin - S. Shnider: Some stable results on t …
Rocky Smith's user avatar