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Noncommutative fibre bundles via bimodules

Edwin Beggs Orcid Logo, JAMES BLAKE

Journal of Pure and Applied Algebra, Volume: 229, Issue: 11, Start page: 108088

Swansea University Authors: Edwin Beggs Orcid Logo, JAMES BLAKE

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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...

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Published in: Journal of Pure and Applied Algebra
ISSN: 0022-4049 1873-1376
Published: Elsevier BV 2025
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URI: https://cronfa.swan.ac.uk/Record/cronfa70347
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spelling 2025-10-02T14:49:28.8297137 v2 70347 2025-09-15 Noncommutative fibre bundles via bimodules a0062e7cf6d68f05151560cdf9d14e75 0000-0002-3139-0983 Edwin Beggs Edwin Beggs true false a3cb2c3bf371160e63e9466f2dd721b5 JAMES BLAKE JAMES BLAKE true false 2025-09-15 MACS 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. Journal Article Journal of Pure and Applied Algebra 229 11 108088 Elsevier BV 0022-4049 1873-1376 Noncommutative differential geometry; Fibre bundles; Spectral sequences; Cohomology; Bimodules 1 11 2025 2025-11-01 10.1016/j.jpaa.2025.108088 COLLEGE NANME Mathematics and Computer Science School COLLEGE CODE MACS Swansea University SU Library paid the OA fee (TA Institutional Deal) The second author acknowledges the support of the UK's EPSRC grant Maths DTP 2020 Swansea University, Grant Ref: EP/V519996/1. 2025-10-02T14:49:28.8297137 2025-09-15T09:39:16.6573850 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Edwin Beggs 0000-0002-3139-0983 1 JAMES BLAKE 2 70347__35229__b8ed587df60f460aaba47d67fef98ba0.pdf 70347.VoR.pdf 2025-10-02T14:44:23.2511291 Output 1158636 application/pdf Version of Record true © 2025 The Author(s). This is an open access article under the CC BY license. true eng http://creativecommons.org/licenses/by/4.0/
title Noncommutative fibre bundles via bimodules
spellingShingle Noncommutative fibre bundles via bimodules
Edwin Beggs
JAMES BLAKE
title_short Noncommutative fibre bundles via bimodules
title_full Noncommutative fibre bundles via bimodules
title_fullStr Noncommutative fibre bundles via bimodules
title_full_unstemmed Noncommutative fibre bundles via bimodules
title_sort Noncommutative fibre bundles via bimodules
author_id_str_mv a0062e7cf6d68f05151560cdf9d14e75
a3cb2c3bf371160e63e9466f2dd721b5
author_id_fullname_str_mv a0062e7cf6d68f05151560cdf9d14e75_***_Edwin Beggs
a3cb2c3bf371160e63e9466f2dd721b5_***_JAMES BLAKE
author Edwin Beggs
JAMES BLAKE
author2 Edwin Beggs
JAMES BLAKE
format Journal article
container_title Journal of Pure and Applied Algebra
container_volume 229
container_issue 11
container_start_page 108088
publishDate 2025
institution Swansea University
issn 0022-4049
1873-1376
doi_str_mv 10.1016/j.jpaa.2025.108088
publisher Elsevier BV
college_str Faculty of Science and Engineering
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hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics
document_store_str 1
active_str 0
description 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.
published_date 2025-11-01T08:25:56Z
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score 11.085163

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