Poisson-like cohomologies associated with some Lie superalgebras

Author:

Kentaro Mikami, Tadayoshi Mizutani, Hajime Sato

Keyword:

Mathematics, Differential Geometry, Differential Geometry (math.DG)

journal:

date:

2023-06-29 16:00:00

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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