Algebra cohomology over a commutative algebra revisited

TL;DR

This paper introduces a simplified bicomplex for computing Shukla or Quillen cohomology of associative algebras over a commutative algebra, specifically when the base algebra is over a field.

Contribution

It provides a more accessible method to compute cohomology in this context by constructing an easier bicomplex.

Findings

Simplified bicomplex for cohomology computation

Applicable to associative algebras over a field

Facilitates easier calculations of Shukla and Quillen cohomology

Abstract

The aim of this paper is to give a relatively easy bicomplex which computes the Shukla, or Quillen cohomology in the category of associative algebras over a commutative algebra $A$, in the case when $A$ is an algebra over a field.