URegina Topology & Geometry Seminar: Ben Willliams

This is joint work with Uriya First. Azumaya algebras are objects that are locally isomorphic to matrix algebras—over a topological space X, they are bundles of matrix algebras. If the base space X is endowed with a self-map of order 2 (which may be trivial) t : X → X, then a t-involution of an Azumaya algebra A over X is a map s : A → A of order 2 that preserves addition, reverses multiplication, and is compatible with t. These involutions are analogues of transposition or hermitian conjugation of matrix algebras. I will explain a coarse classification of these involutions into types, depending on the base involution t, and produce some exotic examples.