Principal non-commutative torus bundles
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In this paper we study continuous bundles of C*-algebras which are non-commutative analogues of principal torus bundles. We show that all such bundles, although in general being very far away from being locally trivial bundles, are at least locally ℛKK-trivial. Using earlier results of Echterhoff and Williams, we shall give a complete classification of principal non-commutative torus bundles up to n-equivariant Morita equivalence. We then study these bundles as topological fibrations (forgetting the group action) and give necessary and sufficient conditions for any non-commutative principal torus bundle being ℛKK-equivalent to a commutative one. As an application of our methods we shall also give a K-theoretic characterization of those principal Tn-bundles with H-flux, as studied by Mathai and Rosenberg which possess 'classical' T-duals.
Original language | English |
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Journal | Proceedings of the London Mathematical Society |
Volume | 99 |
Issue number | 1 |
Pages (from-to) | 1-31 |
Number of pages | 31 |
ISSN | 0024-6115 |
DOIs | |
Publication status | Published - 1 Jul 2009 |
ID: 237364433