BV structure on the Hochschild cohomology of twisted tensor products
Matthew Antrobus
TL;DR
This paper describes how to compute the BV operator on the Hochschild cohomology of twisted tensor products of Frobenius algebras, generalizing previous results and simplifying calculations.
Contribution
It introduces a formula for the BV operator on Hochschild cohomology of twisted tensor products, extending prior work to include twisting by bicharacters.
Findings
Provides a new explicit description of the BV operator for twisted tensor products.
Generalizes previous results to include bicharacter twists.
Simplifies calculations in Hochschild cohomology literature.
Abstract
Given two Frobenius algebras, we describe the BV operator on the Hochschild cohomology of their tensor product twisted by a bicharacter in terms of twisted BV operators on summands of the Hochschild cohomology described by Briggs and Witherspoon. This specialises to the case of non-twisted tensor products, and in doing so generalises a result of Le and Zhou. This allows us to simplify calculations in the literature significantly.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Advanced Operator Algebra Research