Hochschild homology and cohomology for involutive $A_\infty$-algebras

TL;DR

This paper explores the homological properties of bimodules over involutive $A_ abla$-algebras and introduces a derived framework for Hochschild homology and cohomology in this context.

Contribution

It provides a new derived approach to Hochschild (co)homology for involutive $A_ abla$-algebras, extending existing theories.

Findings

Developed a derived description of Hochschild homology for involutive $A_ abla$-algebras

Analyzed bimodule structures over involutive $A_ abla$-algebras

Extended homological algebra tools to involutive $A_ abla$-algebras

Abstract

We present a study of the homological algebra of bimodules over $A_\infty$-algebras endowed with an involution. Furthermore we introduce a derived description of Hochschild homology and cohomology for involutive $A_\infty$-algebras.