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Decomposition of topological Azumaya algebras
- Part of
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- Journal:
- Canadian Mathematical Bulletin / Volume 65 / Issue 2 / June 2022
- Published online by Cambridge University Press:
- 29 June 2021, pp. 506-524
- Print publication:
- June 2022
-
- Article
- Export citation
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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.
