On the Hochschild (co)homology of quantum exterior algebras

TL;DR

This paper computes the Hochschild (co)homology of quantum exterior algebras with twisted bimodule coefficients, revealing diverse homological behaviors of these algebras.

Contribution

It provides explicit calculations of Hochschild (co)homology for quantum exterior algebras, highlighting their complex homological properties.

Findings

Examples of varied homological behaviors of quantum exterior algebras

Explicit Hochschild (co)homology computations with twisted bimodules

Insights into the structure of quantum exterior algebras

Abstract

We compute the Hochschild cohomology and homology of a class of quantum exterior algebras, with coefficients in twisted bimodules. As a result we obtain several interesting examples of the homological behavior of these algebras.