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Noncommutative circle bundles and new Dirac operators

TitleNoncommutative circle bundles and new Dirac operators
Publication TypeJournal Article
Year of Publication2013
AuthorsDabrowski, L, Sitarz, A
JournalCommunications in Mathematical Physics. Volume 318, Issue 1, 2013, Pages 111-130
KeywordsQuantum principal bundles

We study spectral triples over noncommutative principal U(1) bundles. Basing
on the classical situation and the abstract algebraic approach, we propose an
operatorial definition for a connection and compatibility between the
connection and the Dirac operator on the total space and on the base space of
the bundle. We analyze in details the example of the noncommutative three-torus
viewed as a U(1) bundle over the noncommutative two-torus and find all
connections compatible with an admissible Dirac operator. Conversely, we find a
family of new Dirac operators on the noncommutative tori, which arise from the
base-space Dirac operator and a suitable connection.


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