Hochschild cohomology of ℤ_n-Galois coverings of an algebra

Abstract

We consider the ℤ_n-Galois covering Λ_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 Λ_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.

Keywords

Hochschild cohomology / Galois covering / Koszul algebra

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