Cohomology groups of homogeneous Poisson structures
Kentaro Mikami (Akita University), Tadayoshi Mizutani (Saitama, University)
TL;DR
This paper extends the concept of weight in Gelfand-Fuks cohomology to homogeneous Poisson vector spaces and explores combinatorial methods for computing Poisson cohomology groups.
Contribution
It introduces a generalized weight notion for Poisson cohomology and applies combinatorial techniques to analyze these groups.
Findings
Generalization of weight concept for Poisson cohomology
Development of combinatorial approach to compute cohomology groups
Insights into the structure of homogeneous Poisson structures
Abstract
We generalize the notion of weight for Gelfan'd-Fuks cohomology theory of symplectic vector spaces to the homogeneous Poisson vector spaces, and try some combinatorial approach to Poisson cohomology groups.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Algebra and Geometry · Advanced Topics in Algebra