# Topology and Geometry Seminar

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Wed., Oct. 18, 2023 2:00 p.m.
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Location: CL 305
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**Speaker: **Ben Willliams, University of British Columbia

**Title: **Classifying involutions of Azumaya algebras (99 kB)

**Abstract: **

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.

Topology and Geometry Seminar: https://www.reginatopology.ca/seminar