Reduction of Hochschild cohomology over algebras finite over their center

TL;DR

This paper extends a known reduction result for Hochschild cohomology from commutative to noncommutative algebras finite over their center by applying ideas from Grothendieck duality theory.

Contribution

It introduces a novel approach using Grothendieck duality to prove a reduction theorem for Hochschild cohomology in noncommutative algebra.

Findings

Generalizes the Hochschild cohomology reduction to noncommutative algebras

Utilizes concepts from Grothendieck duality theory

Provides a broader framework for Hochschild cohomology analysis

Abstract

We borrow ideas from Grothendieck duality theory to noncommutative algebra, and use them to prove a reduction result for Hochschild cohomology for noncommutative algebras which are finite over their center. This generalizes a result over commutative algebras by Avramov, Iyengar, Lipman and Nayak.