Noncommutative differential calculus on (co)homology of hom-associative\n algebras

2020/09/25 by Apurba Das, Das, Apurba
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2009.12266

openalex publication_date 2020/09/25 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

A hom-associative algebra is an algebra whose associativity is twisted by an\nalgebra homomorphism. It was previously shown by the author that the Hochschild\ncohomology of a hom-associative algebra A carries a Gerstenhaber structure.\nIn this short paper, we show that this Gerstenhaber structure together with\ncertain operations on the Hochschild homology of A makes a noncommutative\ndifferential calculus. As an application, we obtain a Batalin-Vilkovisky\nalgebra structure on the Hochschild cohomology of a regular unital symmetric\nhom-associative algebra.\n

Related

• Gerstenhaber algebra structure on the cohomology of a hom-associative\n algebra
• Noncommutative Differential Calculus Structure on Secondary Hochschild\n (co)homology
• α-type Hochschild cohomology of Hom-associative algebras and Hom-bialgebras
• Homotopy G-algebra structure on the cochain complex of hom-type algebras
• Cohomology and Deformations of Hom-algebras