Cohomology of antiPoisson superalgebra
S.E.Konstein, I.V.Tyutin
TL;DR
This paper investigates the cohomological properties of antiPoisson superalgebras defined on Grassmann-valued functions, providing insights into their structure and lower cohomologies.
Contribution
It computes the lower cohomologies of antiPoisson superalgebras on Grassmann-valued functions, a novel analysis in this algebraic context.
Findings
Lower cohomologies of antiPoisson superalgebras are determined.
Results apply to superalgebras on smooth Grassmann-valued functions with compact support.
Provides foundational understanding for further algebraic and geometric studies.
Abstract
We consider antiPoisson superalgebras realized on the smooth Grassmann-valued functions with compact supports in R^n and with the grading inverse to Grassmanian parity. The lower cohomologies of these superalgebras are found.
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