Cohomologies of superalgebra of pointwise superproduct
S. E. Konstein, I. V. Tyutin
TL;DR
This paper investigates the Hochschild cohomologies of a superalgebra formed by smooth Grassmann-valued functions with compact support in R^n, providing new insights into its algebraic structure.
Contribution
It computes the lower Hochschild cohomologies of a specific associative superalgebra, a novel contribution to superalgebra cohomology theory.
Findings
Lower Hochschild cohomologies are explicitly determined.
The superalgebra's algebraic properties are characterized.
Results contribute to understanding superalgebra deformations.
Abstract
We consider associative superalgebra realized on the smooth Grassmann-valued functions with compact supports in R^n. The lower Hochschild cohomologies of this superalgebra are found.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology