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Decomposition of topological Azumaya algebras

Part of: Homotopy groups Homotopy theory Operations and obstructions

Published online by Cambridge University Press:  29 June 2021

Niny Arcila-Maya
Niny Arcila-Maya*
Affiliation:
Department of Mathematics, The University of British Columbia, Room 121, 1984 Mathematics Road, Vancouver, BCV6T 1Z2, Canada
*
ninyam@math.ubc.ca
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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.

Keywords

Topological Azumaya algebraprojective unitary group

MSC classification

Primary: 55P99: None of the above, but in this section
Secondary: 55Q52: Homotopy groups of special spaces 55S45: Postnikov systems, $k$-invariants 16H05: Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.)
Type
Article
Information
Canadian Mathematical Bulletin , Volume 65 , Issue 2 , June 2022 , pp. 506 - 524
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Copyright
© Canadian Mathematical Society 2021

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