Principal non-commutative torus bundles
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Principal non-commutative torus bundles. / Echterhoff, Siegfried; Nest, Ryszard; Oyono-Oyono, Herve.
In: Proceedings of the London Mathematical Society, Vol. 99, No. 1, 01.07.2009, p. 1-31.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - Principal non-commutative torus bundles
AU - Echterhoff, Siegfried
AU - Nest, Ryszard
AU - Oyono-Oyono, Herve
PY - 2009/7/1
Y1 - 2009/7/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=67650189073&partnerID=8YFLogxK
U2 - 10.1112/plms/pdn050
DO - 10.1112/plms/pdn050
M3 - Journal article
AN - SCOPUS:67650189073
VL - 99
SP - 1
EP - 31
JO - Proceedings of the London Mathematical Society
JF - Proceedings of the London Mathematical Society
SN - 0024-6115
IS - 1
ER -
ID: 237364433