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An algebraic framework for noncommutative bundles with homogeneous fibres

Tomasz Brzezinski Orcid Logo, Wojciech Szymański

Algebra & Number Theory, Volume: 15, Issue: 1, Pages: 217 - 240

Swansea University Author: Tomasz Brzezinski Orcid Logo

Abstract

An algebraic framework for noncommutative bundles with (quantum) homogeneous fibres is proposed. The framework relies on the use of principal coalgebra extensions which play the role of principal bundles in noncommutative geometry which might be additionally equipped with a Hopf algebra symmetry. Th...

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Published in: Algebra & Number Theory
ISSN: 1937-0652 1944-7833
Published: Mathematical Sciences Publishers 2021
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URI: https://cronfa.swan.ac.uk/Record/cronfa54834
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spelling 2021-09-20T17:30:57.8425551 v2 54834 2020-07-30 An algebraic framework for noncommutative bundles with homogeneous fibres 30466d840b59627325596fbbb2c82754 0000-0001-6270-3439 Tomasz Brzezinski Tomasz Brzezinski true false 2020-07-30 SMA An algebraic framework for noncommutative bundles with (quantum) homogeneous fibres is proposed. The framework relies on the use of principal coalgebra extensions which play the role of principal bundles in noncommutative geometry which might be additionally equipped with a Hopf algebra symmetry. The proposed framework is supported by two examples of noncommutative $\mathbb{C} P_q^1$-bundles: the quantum flag manifold viewed as a bundle with a generic Podle\'s sphere as a fibre, and the quantum twistor bundle viewed as a bundle over the quantum 4-sphere of Bonechi, Ciccoli and Tarlini. Journal Article Algebra & Number Theory 15 1 217 240 Mathematical Sciences Publishers 1937-0652 1944-7833 noncommutative bundle, quantum flag manifold, quantum homogeneous space, quantum twistor bundle 17 3 2021 2021-03-17 10.2140/ant.2021.15.217 COLLEGE NANME Mathematics COLLEGE CODE SMA Swansea University 2021-09-20T17:30:57.8425551 2020-07-30T15:59:32.7175757 College of Science Mathematics Tomasz Brzezinski 0000-0001-6270-3439 1 Wojciech Szymański 2 54834__17813__d1565bf9d4d74f99a348eabfc73b2b8a.pdf homog-bundle_ANT.pdf 2020-07-30T16:05:03.7269276 Output 375725 application/pdf Accepted Manuscript true true eng
title An algebraic framework for noncommutative bundles with homogeneous fibres
spellingShingle An algebraic framework for noncommutative bundles with homogeneous fibres
Tomasz Brzezinski
title_short An algebraic framework for noncommutative bundles with homogeneous fibres
title_full An algebraic framework for noncommutative bundles with homogeneous fibres
title_fullStr An algebraic framework for noncommutative bundles with homogeneous fibres
title_full_unstemmed An algebraic framework for noncommutative bundles with homogeneous fibres
title_sort An algebraic framework for noncommutative bundles with homogeneous fibres
author_id_str_mv 30466d840b59627325596fbbb2c82754
author_id_fullname_str_mv 30466d840b59627325596fbbb2c82754_***_Tomasz Brzezinski
author Tomasz Brzezinski
author2 Tomasz Brzezinski
Wojciech Szymański
format Journal article
container_title Algebra & Number Theory
container_volume 15
container_issue 1
container_start_page 217
publishDate 2021
institution Swansea University
issn 1937-0652
1944-7833
doi_str_mv 10.2140/ant.2021.15.217
publisher Mathematical Sciences Publishers
college_str College of Science
hierarchytype
hierarchy_top_id collegeofscience
hierarchy_top_title College of Science
hierarchy_parent_id collegeofscience
hierarchy_parent_title College of Science
department_str Mathematics{{{_:::_}}}College of Science{{{_:::_}}}Mathematics
document_store_str 1
active_str 0
description An algebraic framework for noncommutative bundles with (quantum) homogeneous fibres is proposed. The framework relies on the use of principal coalgebra extensions which play the role of principal bundles in noncommutative geometry which might be additionally equipped with a Hopf algebra symmetry. The proposed framework is supported by two examples of noncommutative $\mathbb{C} P_q^1$-bundles: the quantum flag manifold viewed as a bundle with a generic Podle\'s sphere as a fibre, and the quantum twistor bundle viewed as a bundle over the quantum 4-sphere of Bonechi, Ciccoli and Tarlini.
published_date 2021-03-17T04:09:37Z
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score 10.898751