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Decomposition of topological Azumaya algebras
Published online by Cambridge University Press: 29 June 2021
Abstract
Let $\mathscr {A}$ be a topological Azumaya algebra of degree $mn$ over a CW complex X. We give conditions for the positive integers m and n, and the space X so that $\mathscr {A}$ can be decomposed as the tensor product of topological Azumaya algebras of degrees m and n. Then we prove that if $m<n$ and the dimension of X is higher than $2m+1$ , $\mathscr {A}$ may not have such decomposition.
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- © Canadian Mathematical Society 2021