Poisson-like cohomologies associated with some Lie superalgebras
Kentaro Mikami, Tadayoshi Mizutani, and Hajime Sato

TL;DR
This paper generalizes Poisson cohomology to Lie superalgebras, linking it with de Rham cohomology and introducing a new perspective on Euler numbers in superalgebra contexts.
Contribution
It introduces Poisson-like cohomology groups for Lie superalgebras, extending classical Poisson cohomology concepts and relating them to de Rham cohomology.
Findings
Poisson-like cohomology groups generalize classical Poisson cohomology.
De Rham cohomology matches Poisson-like cohomology for differential forms.
New insights into Euler numbers within Lie superalgebra frameworks.
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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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Carbohydrate Chemistry and Synthesis
