Journal article 159 views 39 downloads
Noncommutative fibre bundles via bimodules
,
JAMES BLAKE
Journal of Pure and Applied Algebra, Volume: 229, Issue: 11, Start page: 108088
Swansea University Authors:
Edwin Beggs , JAMES BLAKE
-
PDF | Version of Record
© 2025 The Author(s). This is an open access article under the CC BY license.
Download (1.1MB)
DOI (Published version): 10.1016/j.jpaa.2025.108088
Abstract
We construct a Leray-Serre spectral sequence for fibre bundles for de Rham sheaf cohomology on noncommutative algebras. The morphisms are bimodules with zero-curvature extendable bimodule connections. This generalises definitions involving differentiable algebra maps to differentiable completely pos...
| Published in: | Journal of Pure and Applied Algebra |
|---|---|
| ISSN: | 0022-4049 1873-1376 |
| Published: |
Elsevier BV
2025
|
| Online Access: |
Check full text
|
| URI: | https://cronfa.swan.ac.uk/Record/cronfa70347 |
| Abstract: |
We construct a Leray-Serre spectral sequence for fibre bundles for de Rham sheaf cohomology on noncommutative algebras. The morphisms are bimodules with zero-curvature extendable bimodule connections. This generalises definitions involving differentiable algebra maps to differentiable completely positive maps by using the KSGNS construction and Hilbert C∗-bimodules with bimodule connections. We give examples of noncommutative fibre bundles, involving group algebras, matrix algebras, and the quantum torus. |
|---|---|
| Keywords: |
Noncommutative differential geometry; Fibre bundles; Spectral sequences; Cohomology; Bimodules |
| College: |
Faculty of Science and Engineering |
| Funders: |
The second author acknowledges the support of the UK's EPSRC grant Maths DTP 2020 Swansea University, Grant Ref: EP/V519996/1. |
| Issue: |
11 |
| Start Page: |
108088 |