Journal article 1430 views
Line bundles and the Thom construction in noncommutative geometry
Journal of Noncommutative Geometry, Volume: 8, Issue: 1, Pages: 61 - 105
Swansea University Authors:
Edwin Beggs , Tomasz Brzezinski
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DOI (Published version): 10.4171/JNCG/149
Abstract
The idea of Morita context is used to define a line module (equivalent of a line bundle in noncommutative geometry). Two algebras are constructed from Morita contexts: The first is integer graded, and is a Hopf Galios extension of the original algebra. Given a star structure on the line module, we c...
Published in: | Journal of Noncommutative Geometry |
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ISSN: | 1661-6952 1661-6960 |
Published: |
2014
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URI: | https://cronfa.swan.ac.uk/Record/cronfa13888 |
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2015-07-31T16:33:52.6322321 v2 13888 2013-01-15 Line bundles and the Thom construction in noncommutative geometry a0062e7cf6d68f05151560cdf9d14e75 0000-0002-3139-0983 Edwin Beggs Edwin Beggs true false 30466d840b59627325596fbbb2c82754 0000-0001-6270-3439 Tomasz Brzezinski Tomasz Brzezinski true false 2013-01-15 SMA The idea of Morita context is used to define a line module (equivalent of a line bundle in noncommutative geometry). Two algebras are constructed from Morita contexts: The first is integer graded, and is a Hopf Galios extension of the original algebra. Given a star structure on the line module, we construct a positive integer graded module. This corresponds to the topological Thom construction and associated circle bundle for a line bundle. In the case that the original algebra is a C* algebra, with some positivity assumptions, the Thom construction gives another C* algebra.The paper ends by a study of the de Rham characteristic classes of a NC line module using the methods of Kobayashi and Nomizu. Journal Article Journal of Noncommutative Geometry 8 1 61 105 1661-6952 1661-6960 Noncommutative geometry, line bundle, Chern class, Thom construction 31 12 2014 2014-12-31 10.4171/JNCG/149 http://www.ems-ph.org/journals/journal.php?jrn=JNCG Accepted for publication May 2012. COLLEGE NANME Mathematics COLLEGE CODE SMA Swansea University 2015-07-31T16:33:52.6322321 2013-01-15T09:36:46.5773307 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Edwin Beggs 0000-0002-3139-0983 1 Tomasz Brzeziński 2 Tomasz Brzezinski 0000-0001-6270-3439 3 |
title |
Line bundles and the Thom construction in noncommutative geometry |
spellingShingle |
Line bundles and the Thom construction in noncommutative geometry Edwin Beggs Tomasz Brzezinski |
title_short |
Line bundles and the Thom construction in noncommutative geometry |
title_full |
Line bundles and the Thom construction in noncommutative geometry |
title_fullStr |
Line bundles and the Thom construction in noncommutative geometry |
title_full_unstemmed |
Line bundles and the Thom construction in noncommutative geometry |
title_sort |
Line bundles and the Thom construction in noncommutative geometry |
author_id_str_mv |
a0062e7cf6d68f05151560cdf9d14e75 30466d840b59627325596fbbb2c82754 |
author_id_fullname_str_mv |
a0062e7cf6d68f05151560cdf9d14e75_***_Edwin Beggs 30466d840b59627325596fbbb2c82754_***_Tomasz Brzezinski |
author |
Edwin Beggs Tomasz Brzezinski |
author2 |
Edwin Beggs Tomasz Brzeziński Tomasz Brzezinski |
format |
Journal article |
container_title |
Journal of Noncommutative Geometry |
container_volume |
8 |
container_issue |
1 |
container_start_page |
61 |
publishDate |
2014 |
institution |
Swansea University |
issn |
1661-6952 1661-6960 |
doi_str_mv |
10.4171/JNCG/149 |
college_str |
Faculty of Science and Engineering |
hierarchytype |
|
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facultyofscienceandengineering |
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Faculty of Science and Engineering |
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facultyofscienceandengineering |
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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://www.ems-ph.org/journals/journal.php?jrn=JNCG |
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description |
The idea of Morita context is used to define a line module (equivalent of a line bundle in noncommutative geometry). Two algebras are constructed from Morita contexts: The first is integer graded, and is a Hopf Galios extension of the original algebra. Given a star structure on the line module, we construct a positive integer graded module. This corresponds to the topological Thom construction and associated circle bundle for a line bundle. In the case that the original algebra is a C* algebra, with some positivity assumptions, the Thom construction gives another C* algebra.The paper ends by a study of the de Rham characteristic classes of a NC line module using the methods of Kobayashi and Nomizu. |
published_date |
2014-12-31T03:15:52Z |
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1763750290811518976 |
score |
11.021648 |