Decomposition of Topological Azumaya Algebras with Orthogonal Involution

TL;DR

This paper investigates conditions under which topological Azumaya algebras with orthogonal involutions can be decomposed into tensor products of smaller degree algebras, extending understanding of their structure over CW complexes.

Contribution

It provides new criteria for decomposing topological Azumaya algebras with orthogonal involutions into tensor products of lower degree algebras.

Findings

Established conditions for decomposition based on algebra degrees and CW complex dimension

Extended algebraic decomposition results to topological Azumaya algebras with involutions

Enhanced understanding of the structure of topological Azumaya algebras in topology

Abstract

Let $\mathcal{A}$ be a topological Azumaya algebra of degree $mn$ with an orthogonal involution over a CW complex $X$ of dimension less than or equal to $\min\{m,n\}$. We give conditions for the positive integers $m$ and $n$ so that $\mathcal{A}$ can be decomposed as the tensor product of topological Azumaya algebras of degrees $m$ and $n$ with orthogonal involutions.