Cyclic homology for Hom-associative algebras

TL;DR

This paper extends noncommutative geometry tools like Hochschild and cyclic homology to Hom-associative algebras, which feature a twisted associativity via a homomorphism, broadening the scope of algebraic analysis.

Contribution

It introduces definitions and frameworks for Hochschild, cyclic, and periodic cyclic homology in the context of Hom-associative algebras, generalizing classical theories.

Findings

Established Hochschild homology for Hom-associative algebras

Defined cyclic and periodic cyclic homology in this new setting

Provided foundational tools for noncommutative geometry of Hom-associative structures

Abstract

In the present paper we investigate the noncommutative geometry of a class of algebras, called the Hom-associative algebras, whose associativity is twisted by a homomorphism. We define the Hochschild, cyclic, and periodic cyclic homology and cohomology for this class of algebras generalizing these theories from the associative to the Hom-associative setting.