Classifying Matrix-Valued Holomorphic Cross-Sections Over An Annulus Up To Complete Isometric Isomorphism

Jacob Cornejo; Kathryn McCormick

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arXiv · 2310.14502

Classifying Matrix-Valued Holomorphic Cross-Sections Over An Annulus Up To Complete Isometric Isomorphism

Jacob Cornejo·Kathryn McCormick

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Abstract

We classify certain algebras of matrix-valued cross-sections over an annulus up to complete isometric isomorphism, based on topological bundle invariants. In particular, we study sections of matrix bundles which are continuous on the closure of the annulus and holomorphic on its interior. Our strategy includes exploiting the relationship between concomitants and modulus automorphic functions, as well as the classification of $n$-homogeneous $C^*$-algebras by Fell and Tomiyama-Takesaki. Furthermore, we describe a partial extension of our results over the annulus to larger classes of finitely and smoothly bordered planar domains.

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BibTeX RIS

Jacob Cornejo, Kathryn McCormick. 2023-10-23. Classifying Matrix-Valued Holomorphic Cross-Sections Over An Annulus Up To Complete Isometric Isomorphism. https://arxiv.org/abs/2310.14502

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