Deformations of Azumaya algebras

TL;DR

This paper investigates how Azumaya algebras on manifolds deform, providing insights into their structural flexibility and potential applications in geometry and algebra.

Contribution

It explicitly computes the deformation theory of Azumaya algebras on smooth or complex manifolds, a specialized and previously less understood area.

Findings

Deformation space characterized for Azumaya algebras

Identification of obstructions to deformations

Connections to geometric structures on manifolds

Abstract

In this paper we compute the deformation theory of a special class of algebras, namely of Azumaya algebras on a manifold ($C^{\infty}$ or complex analytic).