Batalin-Vilkovisky structure on Hochschild cohomology with coefficients in the dual algebra

2018/10/30 by Marco Armenta, Armenta, Marco, Leblanc, Samuel
Mathematics · #16E40 (primary) 16G20 (secondary) #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #K-Theory and Homology (math.KT)

paper · pdf · doi:10.48550/arxiv.1810.13023

openalex publication_date 2018/10/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that Hochschild cohomology with coefficients in A^*=\Hom_k(A,k) under conditions on the algebra structure of A^* is a Batalin-Vilkovisky algebra. We also show that for symmetric and Frobenius algebras, this recovers the known BV-structures in Hochschild cohomology with coefficients in A but admits an easy-to-describe BV-operator. Finally, we show that for monomial algebras A = kQ/⟨ T ⟩, the Hochschild cohomology with coefficients in A^* is always a Batalin-Vilkovisky algebra.

Citations

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

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