The Hochschild cohomlogy ring of a self-injective Nakayama algebra is a Batalin-Vilkovisky algebra
Lambre, Zhou and Zimmermann showed that the Hochschild cohomology ring of a Frobenius algebra with semisimple Nakayama automorphism is a Batalin-Vilkovisky algebra. They asked whether the semisimplicity condition is necessary. In this paper, we show that for a self-injective Nakayama algebra, the Hochschild cohomology ring is always a Batalin-Vilkovisky algebra. In course of proofs, we correct some inaccuracies in the literature, hoping not to introduce new errors.
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