Decomposition of topological Azumaya algebras in the stable range

Niny Arcila-Maya (Duke University)

Slides

Topological Azumaya algebras are topological shadows of more complicated algebraic Azumaya algebras defined over, for example, schemes. Tensor product is a well-defined operation on topological Azumaya algebras. Hence given a topological Azumaya algebra A of degree mn, where m and n are positive integers, it is a natural question to ask whether A can be decomposed according to this factorization of mn. In this talk, I explain the definition of a topological Azumaya algebra over a topological space X, and present a result about what conditions should m, n, and X satisfy so that A can be decomposed.