A geometric approach to noncommutative principal torus bundles

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A geometric approach to noncommutative principal torus bundles. / Wagner, Stefan.

I: Proceedings of the London Mathematical Society, Bind 106, Nr. 6, 2013, s. 1179-1222.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Wagner, S 2013, 'A geometric approach to noncommutative principal torus bundles', Proceedings of the London Mathematical Society, bind 106, nr. 6, s. 1179-1222. https://doi.org/10.1112/plms/pds073

APA

Wagner, S. (2013). A geometric approach to noncommutative principal torus bundles. Proceedings of the London Mathematical Society, 106(6), 1179-1222. https://doi.org/10.1112/plms/pds073

Vancouver

Wagner S. A geometric approach to noncommutative principal torus bundles. Proceedings of the London Mathematical Society. 2013;106(6):1179-1222. https://doi.org/10.1112/plms/pds073

Author

Wagner, Stefan. / A geometric approach to noncommutative principal torus bundles. I: Proceedings of the London Mathematical Society. 2013 ; Bind 106, Nr. 6. s. 1179-1222.

Bibtex

@article{713b692126cf4236a32479dc4634ce87,
title = "A geometric approach to noncommutative principal torus bundles",
abstract = "A (smooth) dynamical system with transformation group 핋n is a triple (A, 핋n,α), consisting of a unital locally convex algebra A, the n-torus 핋n and a group homomorphism α:핋n→Aut(A), which induces a (smooth) continuous action of 핋n on A. In this paper, we present a new, geometrically oriented approach to the noncommutative geometry of principal torus bundles based on such dynamical systems. Our approach is inspired by the classical setting: In fact, after recalling the definition of a trivial noncommutative principal torus bundle, we introduce a convenient (smooth) localization method for noncommutative algebras and say that a dynamical system (A, 핋n,α) is called a noncommutative principal 핋n-bundle, if localization leads to a trivial noncommutative principal 핋n-bundle. We prove that this approach extends the classical theory of principal torus bundles and present a bunch of (nontrivial) noncommutative examples.",
author = "Stefan Wagner",
year = "2013",
doi = "10.1112/plms/pds073",
language = "English",
volume = "106",
pages = "1179--1222",
journal = "Proceedings of the London Mathematical Society",
issn = "0024-6115",
publisher = "Oxford University Press",
number = "6",

}

RIS

TY - JOUR

T1 - A geometric approach to noncommutative principal torus bundles

AU - Wagner, Stefan

PY - 2013

Y1 - 2013

N2 - A (smooth) dynamical system with transformation group 핋n is a triple (A, 핋n,α), consisting of a unital locally convex algebra A, the n-torus 핋n and a group homomorphism α:핋n→Aut(A), which induces a (smooth) continuous action of 핋n on A. In this paper, we present a new, geometrically oriented approach to the noncommutative geometry of principal torus bundles based on such dynamical systems. Our approach is inspired by the classical setting: In fact, after recalling the definition of a trivial noncommutative principal torus bundle, we introduce a convenient (smooth) localization method for noncommutative algebras and say that a dynamical system (A, 핋n,α) is called a noncommutative principal 핋n-bundle, if localization leads to a trivial noncommutative principal 핋n-bundle. We prove that this approach extends the classical theory of principal torus bundles and present a bunch of (nontrivial) noncommutative examples.

AB - A (smooth) dynamical system with transformation group 핋n is a triple (A, 핋n,α), consisting of a unital locally convex algebra A, the n-torus 핋n and a group homomorphism α:핋n→Aut(A), which induces a (smooth) continuous action of 핋n on A. In this paper, we present a new, geometrically oriented approach to the noncommutative geometry of principal torus bundles based on such dynamical systems. Our approach is inspired by the classical setting: In fact, after recalling the definition of a trivial noncommutative principal torus bundle, we introduce a convenient (smooth) localization method for noncommutative algebras and say that a dynamical system (A, 핋n,α) is called a noncommutative principal 핋n-bundle, if localization leads to a trivial noncommutative principal 핋n-bundle. We prove that this approach extends the classical theory of principal torus bundles and present a bunch of (nontrivial) noncommutative examples.

U2 - 10.1112/plms/pds073

DO - 10.1112/plms/pds073

M3 - Journal article

VL - 106

SP - 1179

EP - 1222

JO - Proceedings of the London Mathematical Society

JF - Proceedings of the London Mathematical Society

SN - 0024-6115

IS - 6

ER -

ID: 117189788