BV-differential on Hochschild cohomology of Frobenius algebras

2014/05/20 by Yury Volkov, Volkov, Yury
Mathematics · #16E40 #FOS: Mathematics #K-Theory and Homology (math.KT) #Rings and Algebras (math.RA) #math.KT #math.RA #msc:16E40

paper · pdf · doi:10.48550/arxiv.1405.5155

17 pages

arxiv created 2014/05/20 · arxiv updated 2014/05/21

Abstract

For a finite-dimensional Frobenius k-algebra R with the Nakayama automorphism ν we define an algebra \rm HH^*(R)^ν\uparrow. If the order of ν is not divisible by the characteristic of k, this algebra is isomorphic to the Hochschild cohomology algebra of R.. We prove that this algebra is a BV-algebra. We use this fact to calculate the Gerstenhaber algebra structure and BV-structure on the Hochschild cohomology algebras of a family of self-injective algebras of tree type D_n.

Related

• Hochschild cohomology of Frobenius algebras
• The action of the Nakayama automorphism of a Frobenius algebra on Hochschild cohomology
• On algebraic structures of the Hochschild complex
• The Hochschild cohomology ring of a Frobenius algebra with semisimple Nakayama automorphism is a Batalin-Vilkovisky algebra
• The BV Algebra on Hochschild Cohomology Induced by Infinity Inner Products