Cohomology of Restricted Poisson algebras in characteristic 2

2025/04/10 by Bouarroudj, Sofiane, Ehret, Quentin, Liu, Jiefeng · 2 citations
#17B50 #17B56 #17B60 #17B63 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2504.07601

Abstract

In this paper, we study restricted Poisson algebras in characteristic 2 and their relationship with restricted Lie-Rinehart algebras, for which we develop a cohomology theory and investigate abelian extensions. We also construct a full cohomology complex for restricted Poisson algebras in characteristic 2 that captures formal deformations and prove that it is isomorphic to the cohomology complex of a suitable restricted Lie-Rinehart algebra, under certain assumptions. A number of examples are provided in order to illustrate our constructions.

Cited by

• On Poisson superalgebras in characteristic 2
• The Superization of Hochschild's Lemma and Restricted Lie-Rinehart Superalgebras

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