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arXiv · 2504.07601

Cohomology of Restricted Poisson algebras in characteristic 2

Sofiane Bouarroudj·Quentin Ehret·Jiefeng Liu
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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.

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BibTeXRIS

Sofiane Bouarroudj, Quentin Ehret, Jiefeng Liu. 2025-04-10. Cohomology of Restricted Poisson algebras in characteristic 2. https://arxiv.org/abs/2504.07601

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