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arXiv · 1909.05476

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

Mamta Balodi·Abhishek Banerjee·Anita Naolekar
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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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Mamta Balodi, Abhishek Banerjee, Anita Naolekar. 2019-09-12. Weak comp algebras and cup products in secondary Hochschild cohomology of entwining structures. https://arxiv.org/abs/1909.05476

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