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Arcila Maya, Niny Johanna

University of British Columbia

In this thesis, we establish decomposition theorems for topological Azumaya algebras, and topological Azumaya algebras with involutions of the first kind. Decomposition of topological Azumaya algebras Let A be a topological Azumaya algebra of degree mn over a CW complex X. We prove that if m and n are relatively prime, m<n, and the dimension of X is in the stable range for GL(m,ℂ), then A can be decomposed as the tensor product of topological Azumaya algebras of degrees m and n. Moreover, if the dimension of X is outside of the stable range for GL(m,ℂ), then A may not have such a decomposition. Decomposition of topological Azumaya algebras with involution Let A be a topological Azumaya algebra of degree mn with an orthogonal involution over a CW complex X. We prove that if m and n are relatively prime, m<n, and the dimension of X is in the stable range for O(m,ℂ), then A can be decomposed as the tensor product of topological Azumaya algebras of degrees m and n with orthogonal involutions. Let A be a topological Azumaya algebra of degree 2mn with a symplectic involution over a CW complex X. We prove that if n is odd, and dim(X)≤7, then A can be decomposed as the tensor product of a topological Azumaya of degree 2m with a symplectic involution, and a topological Azumaya algebra of degree n with an orthogonal involution.

Text

2021-08-27

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/79489

Mathematics

University of British Columbia

UBCV

http://creativecommons.org/licenses/by-nc-nd/4.0/