Involutions of (Topological) Azumaya Algebras

An Azumaya algebra of degree \(n\) on a ringed space \(X\) is a bundle of algebras that are locally isomorphic to the algebra of \(n\times n\) matrices. These generalize central simple algebras over fields. In this talk, I will concentrate on the topological case where \(X\) is a CW complex.

An involution of an algebra is an additive automorphism of order 2 that reverses multiplication. At one extreme, involutions of the first kind fix \(X\). At the other, involutions of the second kind act freely on \(X\). In between, there are many examples of involutions that are of neither kind.

In this talk, I will construct such examples and describe how we may classify them.

This work is part of a joint project with Uriya First.