Weak comp algebras and cup products in secondary Hochschild cohomology of entwining structures

Abstract

We define the secondary Hochschild complex for an entwining structure over a commutative $k$-algebra $B$. We show that this complex carries the structure of a weak comp algebra. We obtain two distinct cup product structures for the secondary cohomology groups. We also consider a subcomplex on which the two cup products coincide and which satisfies the axioms for being a comp algebra. The cohomology of this subcomplex then forms a Gerstenhaber algebra. We also construct a bicomplex that controls the deformations of the entwining structure over $B$.

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Cited by in corpus (1)

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