Classical Whitehead lemma states that if $\mathfrak g$ is a finite-dimensional complex Lie algebra and $M$ is a finite-dimensional $\mathfrak g$-module, then first cohomology group $H^1(\mathfrak g, M)$ (defined for example as cohomology of the Chevalley-Eilenberg complex) is trivial. I need to know if this is also true for super Lie algebras.
2026-02-22 21:30:29.1771795829
Is Whitehead lemma true for super Lie algebras?
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The Whitehead Lemmas no longer hold for simple Lie superalgebras.
Reference: Representations of algebraic groups, quantum groups and Lie algebras, page $121$.