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

Abstract

Analogous to a recent result of N. Kowalzig and U. Krähmer 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 Koszul duals of Koszul Artin-Schelter regular algebras of dimension three.

References in corpus (3)

• Calabi-Yau algebras
• Noncommutative differential calculus, homotopy BV algebras and formality conjectures
• The Nakayama automorphism of the almost Calabi-Yau algebras associated to SU(3) modular invariants

Cited by in corpus (10)

• Hochschild cohomology of some quantum complete intersections
• Tate-Hochschild Cohomology of Radical Square Zero Algebras
• Hochschild (co)homologies of dg $K$-rings and their Koszul duals
• Batalin-Vilkovisky algebras and the noncommutative Poincare duality of Koszul Calabi-Yau algebras
• A Geometric Approach to Hochschild Cohomology of the Exterior Algebra
• A Batalin-Vilkovisky structure on the complete cohomology ring of a Frobenius algebra
• Batalin-Vilkovisky structure on Hochschild cohomology with coefficients in the dual algebra
• Endomorphism operads of functors
• Koszul duality and the Hochschild cohomology of Artin-Schelter regular algebras
• Batalin--Vilkovisky algebra structures on the Hochschild cohomology of generalized Weyl algebras