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arXiv · 1511.07059

Braided Hochschild cohomology and Hopf actions

Cris Negron
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Abstract

We show that the braided Hochschild cohomology, of an algebra in a suitably algebraic braided monoidal category, admits a graded ring structure under which it is braided commutative. We then give a canonical identification between the usual Hochschild cohomology ring of a smash product and the (derived) invariants of its braided Hochschild cohomology ring. We apply our results to identify the associative formal deformation theory of a smash product with its formal deformation theory as a module algebra over the given Hopf algebra (when the Hopf algebra is sufficiently semisimple). As a second application we deduce some structural results for the usual Hochschild cohomology of a smash product, and discuss specific implications for finite group actions on smooth affine schemes.

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Cris Negron. 2015-11-22. Braided Hochschild cohomology and Hopf actions. https://arxiv.org/abs/1511.07059

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