Abstract

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

中文翻译：

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关于hom-缔合代数的（协）同调性的非交换微积分

摘要

hom-associative代数是其代数同态被扭曲的代数。作者先前已证明，同缔结合代数A的Hochschild同调带有Gerstenhaber结构。在这篇简短的论文中，我们证明了Gerstenhaber结构以及对A的Hochschild同源性的某些运算构成了非交换微分。作为一种应用，我们在规则unit对称的hom-associative代数的Hochschild谐函数上获得了Batalin-Vilkovisky代数结构。