The Topology of Azumaya Algebras

Speaker: Ben Williams

Date: Fri, Oct 12, 2018

Location: PIMS, University of British Columbia

Conference: UBC-PIMS Mathematical Sciences Faculty Award

Subject: Mathematics, Topology

Class: Scientific

Abstract:

Azumaya algebras over a commutative ring R are generalizations of central simple algebras over a field k, and both are "twisted matrix algebras". In this, they bear the same relationship to a noncommutative ring of matrices Mat_n(k) that a vector bundles (or projective modules) bear to vector spaces. That is, they are bundles of algebras. In this talk, I will show that thinking about Azumaya algebras from the algebraic-topological point of view, as bundles of algebras, is fruitful, both in producing examples of algebras with interesting properties, and in proving certain results about such algebras that are difficult to prove by direct, algebraic methods.