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The Hochschild cohomology ring of a Frobenius algebra with semisimple Nakayama automorphism is a Batalin-Vilkovisky algebra

Abstract : In analogy with a recent result of N. Kowalzig and U. Krahmer for twisted Calabi-Yau algebras, we show that the Hochschild cohomology ring of a Frobenius algebra with semisimple Nakayama automorphism is a Batalin-Vilkovisky algebra, thus generalizing a result of T. Tradler for finite dimensional symmetric algebras. We give a criterion to determine when a Frobenius algebra given by quiver with relations has semisimple Nakayama automorphism and apply it to some known classes of tame Frobenius algebras. We also provide ample examples including quantum complete intersections, finite dimensional Hopf algebras defined over an algebraically closed field of characteristic zero and the Koszul duals of Koszul Artin-Schelter regular algebras of dimension three. (C) 2015 Elsevier Inc. All rights reserved.
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Thierry Lambre, Guodong Zhou, Alexander Zimmermann. The Hochschild cohomology ring of a Frobenius algebra with semisimple Nakayama automorphism is a Batalin-Vilkovisky algebra. Journal of Algebra, Elsevier, 2016, 446, pp.103-131. ⟨10.1016/j.jalgebra.2015.09.018⟩. ⟨hal-03623299⟩

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