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arXiv · 1304.0527

The cup product on Hochschild cohomology via twisting cochains and applications to Koszul rings

Cris Negron
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Abstract

Given an acyclic twisting cochain $\pi:C\to A$, from a curved dg coalgebra $C$ to a dg algebra $A$, we show that the associated twisted hom complex $\mathrm{Hom}^\pi_k(C,A)$ has cohomology equal to the Hochschild cohomology of $A$, as a graded ring. As a corollary we find that the Hochschild cohomology of a Koszul algebra $A$, along with its cup product, is a subquotient of the tensor product algebra $A^!\otimes A$ of $A$ with its Koszul dual.

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Cris Negron. 2013-04-02. The cup product on Hochschild cohomology via twisting cochains and applications to Koszul rings. https://arxiv.org/abs/1304.0527

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