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arXiv · 2306.17409

Poisson-like cohomologies associated with some Lie superalgebras

Kentaro Mikami·Tadayoshi Mizutani·Hajime Sato
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Abstract

The concept of Poisson cohomology groups associated with Poisson manifolds is a part of the theory of Lie superalgebras of vector fields. Therefore, we abstracted them as Poisson-like cohomology groups for general Lie superalgebras. In doing so, we obtained a generalization of the concept of the Euler number. For the Lie superalgebras of differential forms on a manifold, we found the de Rham cohomology groups match with the Poisson-like cohomology groups in the special case. In order to understand the development of the discussion, we presented some simple examples and show ideas of how our discussion unfolds.

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Kentaro Mikami, Tadayoshi Mizutani, Hajime Sato. 2023-06-30. Poisson-like cohomologies associated with some Lie superalgebras. https://arxiv.org/abs/2306.17409

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