Decomposition of Symplectic Vector Bundles and Azumaya Algebras
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918129228054528 |
|---|---|
| author | Arcila-Maya, Niny |
| author_facet | Arcila-Maya, Niny |
| contents | Let $X$ be a connected CW complex. Let $\mathcal{V}$ be a symplectic vector bundle of rank $2mn$ over $X$, and let $\mathcal{A}$ be a topological Azumaya algebra of degree $2mn$ with a symplectic involution over a $X$. We give conditions for the positive integers $m$ and $n$, and the dimension of $X$ so that $\mathcal{V}$ can be decomposed as the tensor product of a symplectic vector bundle of rank $2m$ and an orthogonal vector bundle of rank $n$; and so that $\mathcal{A}$ can be decomposed as the tensor product of topological Azumaya algebras of degrees $2m$ and $n$ with involutions of the first kind. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_17029 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Decomposition of Symplectic Vector Bundles and Azumaya Algebras Arcila-Maya, Niny Algebraic Topology 55P99, 55Q52, 55S35 (Primary), 55S45, 16H05, 16W10 (Secondary) Let $X$ be a connected CW complex. Let $\mathcal{V}$ be a symplectic vector bundle of rank $2mn$ over $X$, and let $\mathcal{A}$ be a topological Azumaya algebra of degree $2mn$ with a symplectic involution over a $X$. We give conditions for the positive integers $m$ and $n$, and the dimension of $X$ so that $\mathcal{V}$ can be decomposed as the tensor product of a symplectic vector bundle of rank $2m$ and an orthogonal vector bundle of rank $n$; and so that $\mathcal{A}$ can be decomposed as the tensor product of topological Azumaya algebras of degrees $2m$ and $n$ with involutions of the first kind. |
| title | Decomposition of Symplectic Vector Bundles and Azumaya Algebras |
| topic | Algebraic Topology 55P99, 55Q52, 55S35 (Primary), 55S45, 16H05, 16W10 (Secondary) |
| url | https://arxiv.org/abs/2311.17029 |