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Line bundles and the Thom construction in noncommutative geometry / Edwin, Beggs; Tomasz, Brzezinski

Journal of Noncommutative Geometry, Volume: 8, Issue: 1, Pages: 61 - 105

Swansesa 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...

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Published in: Journal of Noncommutative Geometry
ISSN: 1661-6952 1661-6960
Published: 2014
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URI: https://cronfa.swan.ac.uk/Record/cronfa13888
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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 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.
Item Description: Accepted for publication May 2012.
Keywords: Noncommutative geometry, line bundle, Chern class, Thom construction
College: College of Science
Issue: 1
Start Page: 61
End Page: 105