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

Harvard

Echterhoff, S, Nest, R & Oyono-Oyono, H 2009, 'Principal non-commutative torus bundles', Proceedings of the London Mathematical Society, vol. 99, no. 1, pp. 1-31. https://doi.org/10.1112/plms/pdn050

APA

Echterhoff, S., Nest, R., & Oyono-Oyono, H. (2009). Principal non-commutative torus bundles. Proceedings of the London Mathematical Society, 99(1), 1-31. https://doi.org/10.1112/plms/pdn050

Vancouver

Echterhoff S, Nest R, Oyono-Oyono H. Principal non-commutative torus bundles. Proceedings of the London Mathematical Society. 2009 Jul 1;99(1):1-31. https://doi.org/10.1112/plms/pdn050

Author

Echterhoff, Siegfried ; Nest, Ryszard ; Oyono-Oyono, Herve. / Principal non-commutative torus bundles. In: Proceedings of the London Mathematical Society. 2009 ; Vol. 99, No. 1. pp. 1-31.

Bibtex

@article{f7731df46be9499aa804b21a7d7d0241,
title = "Principal non-commutative torus bundles",
abstract = "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.",
author = "Siegfried Echterhoff and Ryszard Nest and Herve Oyono-Oyono",
year = "2009",
month = jul,
day = "1",
doi = "10.1112/plms/pdn050",
language = "English",
volume = "99",
pages = "1--31",
journal = "Proceedings of the London Mathematical Society",
issn = "0024-6115",
publisher = "Oxford University Press",
number = "1",

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RIS

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.

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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