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Noncommutative geodesics and the KSGNS construction

Edwin Beggs Orcid Logo

Journal of Geometry and Physics, Volume: 158, Start page: 103851

Swansea University Author: Edwin Beggs Orcid Logo

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DOI (Published version): 10.1016/j.geomphys.2020.103851

Abstract

We study geodesics in noncommutative geometry by means of bimodule connections and completely positive maps using the Kasparov, Stinespring, Gel’fand, Naĭmark & Segal (KSGNS) construction. This is motivated from classical geometry, and we also consider examples on the algebras M_2 and C(Z_n)thou...

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Published in: Journal of Geometry and Physics
ISSN: 0393-0440
Published: Elsevier BV 2020
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URI: https://cronfa.swan.ac.uk/Record/cronfa54891
first_indexed 2020-08-06T12:16:31Z
last_indexed 2020-12-10T04:09:31Z
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spelling 2020-12-09T11:42:58.9694495 v2 54891 2020-08-06 Noncommutative geodesics and the KSGNS construction a0062e7cf6d68f05151560cdf9d14e75 0000-0002-3139-0983 Edwin Beggs Edwin Beggs true false 2020-08-06 MACS We study geodesics in noncommutative geometry by means of bimodule connections and completely positive maps using the Kasparov, Stinespring, Gel’fand, Naĭmark & Segal (KSGNS) construction. This is motivated from classical geometry, and we also consider examples on the algebras M_2 and C(Z_n)though restricting to classical time. On the way we have to consider the reality of a noncommutative vector field, and for this we propose a definition depending on a state on the algebra. Journal Article Journal of Geometry and Physics 158 103851 Elsevier BV 0393-0440 Noncommutative geometry; Differential geometry; Geodesic; Positive map; Hilbert C*module 1 12 2020 2020-12-01 10.1016/j.geomphys.2020.103851 COLLEGE NANME Mathematics and Computer Science School COLLEGE CODE MACS Swansea University 2020-12-09T11:42:58.9694495 2020-08-06T13:11:08.8293308 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Edwin Beggs 0000-0002-3139-0983 1 54891__17875__c7a3f08fb8dd4abab0938d45f17c3cb1.pdf GeodesicSubmit.pdf 2020-08-06T13:13:14.2581696 Output 691285 application/pdf Accepted Manuscript true 2021-08-05T00:00:00.0000000 Released under the terms of a Creative Commons Attribution Non-Commercial No Derivatives License (CC-BY-NC-ND). true English
title Noncommutative geodesics and the KSGNS construction
spellingShingle Noncommutative geodesics and the KSGNS construction
Edwin Beggs
title_short Noncommutative geodesics and the KSGNS construction
title_full Noncommutative geodesics and the KSGNS construction
title_fullStr Noncommutative geodesics and the KSGNS construction
title_full_unstemmed Noncommutative geodesics and the KSGNS construction
title_sort Noncommutative geodesics and the KSGNS construction
author_id_str_mv a0062e7cf6d68f05151560cdf9d14e75
author_id_fullname_str_mv a0062e7cf6d68f05151560cdf9d14e75_***_Edwin Beggs
author Edwin Beggs
author2 Edwin Beggs
format Journal article
container_title Journal of Geometry and Physics
container_volume 158
container_start_page 103851
publishDate 2020
institution Swansea University
issn 0393-0440
doi_str_mv 10.1016/j.geomphys.2020.103851
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
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description We study geodesics in noncommutative geometry by means of bimodule connections and completely positive maps using the Kasparov, Stinespring, Gel’fand, Naĭmark & Segal (KSGNS) construction. This is motivated from classical geometry, and we also consider examples on the algebras M_2 and C(Z_n)though restricting to classical time. On the way we have to consider the reality of a noncommutative vector field, and for this we propose a definition depending on a state on the algebra.
published_date 2020-12-01T13:51:33Z
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