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arXiv · 2206.07943

Cohomology of $\frak{sl}(2)$ and its applications in prime characteristic

Shujuan Wang·Zhaoxin Li
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Abstract

Over a field of characteristic $p>2,$ the first cohomology of the 3-dimensional simple Lie algebra $\frak{sl}(2)$ with coefficients in all simple modules is determined, which implies Whitehead's first lemma is not true in prime characteristic. As applications, derivations and 2-local derivations of $\frak{sl}(2)$ on any simple module are also be characterized.

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BibTeXRIS

Shujuan Wang, Zhaoxin Li. 2022-06-16. Cohomology of $\frak{sl}(2)$ and its applications in prime characteristic. https://arxiv.org/abs/2206.07943

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