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Complex geometry of quantum cones

Tomasz Brzezinski Orcid Logo

Fortschritte der Physik, Volume: 62, Issue: 9-10, Pages: 875 - 880

Swansea University Author: Tomasz Brzezinski Orcid Logo

DOI (Published version): 10.1002/prop.201400051

Abstract

The algebras obtained as fixed points of the action of the cyclic group ZN on the coordinate algebra of the quantum disc are studied. These can be understood as coordinate algebras of quantum or non-commutative cones. The following observations are made. First, contrary to the classical situation, t...

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Published in: Fortschritte der Physik
Published: 2014
Online Access: http://arxiv.org/abs/1406.2517
URI: https://cronfa.swan.ac.uk/Record/cronfa20516
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spelling 2019-06-20T17:20:07.2404603 v2 20516 2015-03-25 Complex geometry of quantum cones 30466d840b59627325596fbbb2c82754 0000-0001-6270-3439 Tomasz Brzezinski Tomasz Brzezinski true false 2015-03-25 SMA The algebras obtained as fixed points of the action of the cyclic group ZN on the coordinate algebra of the quantum disc are studied. These can be understood as coordinate algebras of quantum or non-commutative cones. The following observations are made. First, contrary to the classical situation, the actions of ZN are free and the resulting algebras are homologically smooth. Second, the quantum cone algebras admit differential calculi that have all the characteristics of calculi on smooth complex curves. Third, the corresponding volume forms are exact, indicating that the constructed algebras describe manifolds with boundaries. Journal Article Fortschritte der Physik 62 9-10 875 880 11 9 2014 2014-09-11 10.1002/prop.201400051 http://arxiv.org/abs/1406.2517 COLLEGE NANME Mathematics COLLEGE CODE SMA Swansea University 2019-06-20T17:20:07.2404603 2015-03-25T09:37:14.4463268 College of Science Mathematics Tomasz Brzezinski 0000-0001-6270-3439 1 0020516-26032015103054.pdf cone_rev.pdf 2015-03-26T10:30:54.6970000 Output 125909 application/pdf Accepted Manuscript true 2015-03-26T00:00:00.0000000 true
title Complex geometry of quantum cones
spellingShingle Complex geometry of quantum cones
Tomasz Brzezinski
title_short Complex geometry of quantum cones
title_full Complex geometry of quantum cones
title_fullStr Complex geometry of quantum cones
title_full_unstemmed Complex geometry of quantum cones
title_sort Complex geometry of quantum cones
author_id_str_mv 30466d840b59627325596fbbb2c82754
author_id_fullname_str_mv 30466d840b59627325596fbbb2c82754_***_Tomasz Brzezinski
author Tomasz Brzezinski
author2 Tomasz Brzezinski
format Journal article
container_title Fortschritte der Physik
container_volume 62
container_issue 9-10
container_start_page 875
publishDate 2014
institution Swansea University
doi_str_mv 10.1002/prop.201400051
college_str College of Science
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hierarchy_top_title College of Science
hierarchy_parent_id collegeofscience
hierarchy_parent_title College of Science
department_str Mathematics{{{_:::_}}}College of Science{{{_:::_}}}Mathematics
url http://arxiv.org/abs/1406.2517
document_store_str 1
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description The algebras obtained as fixed points of the action of the cyclic group ZN on the coordinate algebra of the quantum disc are studied. These can be understood as coordinate algebras of quantum or non-commutative cones. The following observations are made. First, contrary to the classical situation, the actions of ZN are free and the resulting algebras are homologically smooth. Second, the quantum cone algebras admit differential calculi that have all the characteristics of calculi on smooth complex curves. Third, the corresponding volume forms are exact, indicating that the constructed algebras describe manifolds with boundaries.
published_date 2014-09-11T03:30:51Z
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