Decomposition of topological Azumaya algebras in the stable range

Wednesday, August 3, 2022 - 1:00pm - 1:45pm
Keller 3-180
Niny Arcila-Maya (Duke University)
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 $\mathcal{A}$ of degree $mn$, where $m$ and $n$ are positive integers, it is a natural question to ask whether $\mathcal{A}$ 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 $\mathcal{A}$ can be decomposed.