Cohomology of \fraksl(2) and its applications in prime characteristic

2022/06/16 by Shujuan Wang, Wang, Shujuan, Zhaoxin Li +1
Mathematics · Physics and Astronomy · #17B40 #17B50 #17B56 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2206.07943

openalex publication_date 2022/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Over a field of characteristic p>2, the first cohomology of the 3-dimensional simple Lie algebra \fraksl(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 \fraksl(2) on any simple module are also be characterized.

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