Hochschild cohomology of {\mathbb{Z}}_{\mathit{n}}-Galois coverings of an algebra

Abstract

We consider the {\mathbb{Z}}_{\mathit{n}}-Galois covering {\mathrm{\Lambda }}_n of the algebra A introduced by F. Xu [Adv. Math., 2008, 219: 1872-1893]. We calculate the dimensions of all Hochschild cohomology groups of {\mathrm{\Lambda }}_n and give the ring structure of the Hochschild cohomology ring modulo nilpotence. As a conclusion, we provide a class of counterexamples to Snashall-Solberg’s conjecture.

Key words： Hochschild cohomology; Galois covering; Koszul algebra

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