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Circle and Line Bundles Over Generalized Weyl Algebras

Tomasz Brzeziński, Tomasz Brzezinski Orcid Logo

Algebras and Representation Theory, Volume: 19, Issue: 1, Pages: 57 - 69

Swansea University Author: Tomasz Brzezinski Orcid Logo

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DOI (Published version): 10.1007/s10468-015-9562-7

Abstract

Strongly Z-graded algebras or principal circle bundles and associated line bundles or invertible bimodules over a class of generalized Weyl algebras B(p;q,0) (over a ring of polynomials in one variable) are constructed. The Chern-Connes pairing between the cyclic cohomology of B(p;q,0) and the isomo...

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Published in: Algebras and Representation Theory
ISSN: 1386-923X 1572-9079
Published: 2016
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URI: https://cronfa.swan.ac.uk/Record/cronfa22634
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first_indexed 2015-07-23T02:04:17Z
last_indexed 2018-07-30T12:56:57Z
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spelling 2018-07-30T10:01:45.2569910 v2 22634 2015-07-22 Circle and Line Bundles Over Generalized Weyl Algebras 30466d840b59627325596fbbb2c82754 0000-0001-6270-3439 Tomasz Brzezinski Tomasz Brzezinski true false 2015-07-22 SMA Strongly Z-graded algebras or principal circle bundles and associated line bundles or invertible bimodules over a class of generalized Weyl algebras B(p;q,0) (over a ring of polynomials in one variable) are constructed. The Chern-Connes pairing between the cyclic cohomology of B(p;q,0) and the isomorphism classes of sections of associated line bundles over B(p;q,0) is computed, thus demonstrating that these bundles, which are labelled by integers, are non-trivial and mutually non- isomorphic. The constructed strongly Z-graded algebras are shown to have Hochschild cohomology reminiscent of that of Calabi-Yau algebras. The paper is supplemented by an observation that a grading by an Abelian group in the middle of a short exact sequence is strong if and only if the induced gradings by the outer groups in the sequence are strong. Journal Article Algebras and Representation Theory 19 1 57 69 1386-923X 1572-9079 31 12 2016 2016-12-31 10.1007/s10468-015-9562-7 COLLEGE NANME Mathematics COLLEGE CODE SMA Swansea University 2018-07-30T10:01:45.2569910 2015-07-22T09:10:26.7005454 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Tomasz Brzeziński 1 Tomasz Brzezinski 0000-0001-6270-3439 2 0022634-01052018145427.pdf Weyl_rev-corr.pdf 2018-05-01T14:54:27.5970000 Output 319498 application/pdf Accepted Manuscript true 2018-05-01T00:00:00.0000000 true eng
title Circle and Line Bundles Over Generalized Weyl Algebras
spellingShingle Circle and Line Bundles Over Generalized Weyl Algebras
Tomasz Brzezinski
title_short Circle and Line Bundles Over Generalized Weyl Algebras
title_full Circle and Line Bundles Over Generalized Weyl Algebras
title_fullStr Circle and Line Bundles Over Generalized Weyl Algebras
title_full_unstemmed Circle and Line Bundles Over Generalized Weyl Algebras
title_sort Circle and Line Bundles Over Generalized Weyl Algebras
author_id_str_mv 30466d840b59627325596fbbb2c82754
author_id_fullname_str_mv 30466d840b59627325596fbbb2c82754_***_Tomasz Brzezinski
author Tomasz Brzezinski
author2 Tomasz Brzeziński
Tomasz Brzezinski
format Journal article
container_title Algebras and Representation Theory
container_volume 19
container_issue 1
container_start_page 57
publishDate 2016
institution Swansea University
issn 1386-923X
1572-9079
doi_str_mv 10.1007/s10468-015-9562-7
college_str Faculty of Science and Engineering
hierarchytype
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 Strongly Z-graded algebras or principal circle bundles and associated line bundles or invertible bimodules over a class of generalized Weyl algebras B(p;q,0) (over a ring of polynomials in one variable) are constructed. The Chern-Connes pairing between the cyclic cohomology of B(p;q,0) and the isomorphism classes of sections of associated line bundles over B(p;q,0) is computed, thus demonstrating that these bundles, which are labelled by integers, are non-trivial and mutually non- isomorphic. The constructed strongly Z-graded algebras are shown to have Hochschild cohomology reminiscent of that of Calabi-Yau algebras. The paper is supplemented by an observation that a grading by an Abelian group in the middle of a short exact sequence is strong if and only if the induced gradings by the outer groups in the sequence are strong.
published_date 2016-12-31T03:26:49Z
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