Decomposition of Topological Azumaya Algebras
Niny Arcila-Maya

TL;DR
This paper investigates conditions under which topological Azumaya algebras can be decomposed into tensor products of lower-degree algebras, revealing limitations based on algebra degree and space dimension.
Contribution
It provides new criteria for decomposing topological Azumaya algebras and demonstrates cases where such decompositions are impossible.
Findings
Decomposition criteria depend on algebra degree and space topology.
High-dimensional spaces can prevent algebra decomposition.
Certain degrees of Azumaya algebras cannot be decomposed in specified conditions.
Abstract
Let be a topological Azumaya algebra of degree over a CW complex . We give conditions for the positive integers and , and the space so that can be decomposed as the tensor product of topological Azumaya algebras of degrees and . Then we prove that if and the dimension of is higher than , may not have such decomposition.
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