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The Exponential Map for Hopf Algebras

Ghaliah Alhamzi, Edwin Beggs Orcid Logo

Symmetry, Integrability and Geometry: Methods and Applications, Volume: 18, Issue: 2022

Swansea University Author: Edwin Beggs Orcid Logo

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DOI (Published version): 10.3842/sigma.2022.017

Abstract

We give an analogue of the classical exponential map on Lie groups for Hopf∗-algebras with differential calculus. The major difference with the classical case is the interpretation of the value of the exponential map, classically an element of the Lie group. We give interpretations as states on the...

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Published in: Symmetry, Integrability and Geometry: Methods and Applications
ISSN: 1815-0659
Published: SIGMA (Symmetry, Integrability and Geometry: Methods and Application)
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URI: https://cronfa.swan.ac.uk/Record/cronfa59445
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first_indexed 2022-02-23T15:47:00Z
last_indexed 2023-01-11T14:40:43Z
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spelling 2022-10-27T11:46:50.4483115 v2 59445 2022-02-23 The Exponential Map for Hopf Algebras a0062e7cf6d68f05151560cdf9d14e75 0000-0002-3139-0983 Edwin Beggs Edwin Beggs true false 2022-02-23 SMA We give an analogue of the classical exponential map on Lie groups for Hopf∗-algebras with differential calculus. The major difference with the classical case is the interpretation of the value of the exponential map, classically an element of the Lie group. We give interpretations as states on the Hopf algebra, elements of a Hilbert C ∗-bimodule of 1/2 densities and elements of the dual Hopf algebra. We give examples for complex valued functions on the groups S3 and Z, Woronowicz’s matrix quantum group Cq[SU2] and the Sweedler–Taft algebra. Journal Article Symmetry, Integrability and Geometry: Methods and Applications 18 2022 SIGMA (Symmetry, Integrability and Geometry: Methods and Application) 1815-0659 exponential map, Hopf algebras, geodesic 0 0 0 0001-01-01 10.3842/sigma.2022.017 http://dx.doi.org/10.3842/sigma.2022.017 COLLEGE NANME Mathematics COLLEGE CODE SMA Swansea University 2022-10-27T11:46:50.4483115 2022-02-23T15:40:55.6731089 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Ghaliah Alhamzi 1 Edwin Beggs 0000-0002-3139-0983 2 59445__22445__b1ad4bd704f04c7ebfd7ddaa5b1caeca.pdf The Exponential Map for Hopf Algebra.pdf 2022-02-23T15:44:30.4549961 Output 637218 application/pdf Accepted Manuscript true The authors retain the copyright for their papers published in SIGMA under the terms of the Creative Commons Attribution-ShareAlike License . true eng http://creativecommons.org/licenses/by-sa/4.0/
title The Exponential Map for Hopf Algebras
spellingShingle The Exponential Map for Hopf Algebras
Edwin Beggs
title_short The Exponential Map for Hopf Algebras
title_full The Exponential Map for Hopf Algebras
title_fullStr The Exponential Map for Hopf Algebras
title_full_unstemmed The Exponential Map for Hopf Algebras
title_sort The Exponential Map for Hopf Algebras
author_id_str_mv a0062e7cf6d68f05151560cdf9d14e75
author_id_fullname_str_mv a0062e7cf6d68f05151560cdf9d14e75_***_Edwin Beggs
author Edwin Beggs
author2 Ghaliah Alhamzi
Edwin Beggs
format Journal article
container_title Symmetry, Integrability and Geometry: Methods and Applications
container_volume 18
container_issue 2022
institution Swansea University
issn 1815-0659
doi_str_mv 10.3842/sigma.2022.017
publisher SIGMA (Symmetry, Integrability and Geometry: Methods and Application)
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
url http://dx.doi.org/10.3842/sigma.2022.017
document_store_str 1
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description We give an analogue of the classical exponential map on Lie groups for Hopf∗-algebras with differential calculus. The major difference with the classical case is the interpretation of the value of the exponential map, classically an element of the Lie group. We give interpretations as states on the Hopf algebra, elements of a Hilbert C ∗-bimodule of 1/2 densities and elements of the dual Hopf algebra. We give examples for complex valued functions on the groups S3 and Z, Woronowicz’s matrix quantum group Cq[SU2] and the Sweedler–Taft algebra.
published_date 0001-01-01T04:14:06Z
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