On noncommutative principal bundles with finite abelian structure group

Journal of Noncommutative Geometry

Volumn 8, Issue 4, 2014, Pages 987-1022

  Wagner, Stefan ^a  

^a UNIVERSITY OF HELSINKI   (Finland)

Author keywords

(Trivial) noncommutative principal bundles with finite abelian structure group; (Trivial) principal bundles with finite abelian structure group; Crossed product algebras; Dynamical systems; Factor systems; Graded algebras; Noncommutative differential geometry

Indexed keywords

EID: 84922335666     PISSN: 16616952     EISSN: 16616960     Source Type: Journal    
DOI: 10.4171/JNCG/175     Document Type: Article

References (21)

1. Allison, B., S. Berman and A. Pianzola Covering Algebras II: Isomorphism of Loop algebras, Journal für die reine und angewandte Mathematik (Crelles Journal), 571, (2004), 39-71. Zbl 1056.17018 MR 2070143
2. Baum, P., P. Hajac, R. Matthes and W. Szymanski, Non-commutative geometry approach to principal and associated bundles, arXiv:0701033v2 [math.DG], 8 Jan 2007.
3. Blattner, R. J. and S. Montgomery, A Duality Theorem for Hopf Module Algebras, Journal of Algebra, 95, 153-172, 1985. Zbl 0589.16010 MR 797661
4. Doran, R. S. and J. M. G. Fell, Representations of ∗-algebras, locally compact groups, and Banach ∗-algebraic bundles, Pure and Applied Mathematics vol. 125 and 126, Academic Press, 1988. Volume 1: Zbl 00193042; Volume 2: Zbl 0652.46051
5. Echterhoff, S., Ryszard Nest and Herve Oyono-Oyono, Principal non-commutative torus bundles, in Proceedings of the London Mathematical Society, (3) 99 (2009), 1-31. Zbl 1176.19003 MR 2520349
6. Exel, R., Amenability for Fell Bundles, in Journal für die reine und angewandte Mathematik Crelles Journal, vol. 492, (1996), 1-31. Zbl 0881.46046 MR 1488064
7. Green, P., C∗-algebras of transformation groups with smooth orbit space, Pacific J. Math. 72 (1977), no. 1, 71-97. Zbl 0374.46047 MR 453917
8. Hajac, P. M., Lecture Notes on Noncommutative Geometry and Quantum Groups, Lecture Notes edited by Piotr M. Hajac. Available at: http://www.mimuw.edu.pl/∼pwit/toknotes/toknotes.pdf .
9. Kobayashi, S., and K. Nomizu, Foundations of Differential Geometry vol. 1, Interscience Tracts in Pure and Applied Mathematics, Wiley, 1963.
10. Landi, G., and W. van Suijlekom, Principal fibrations from noncommutative spheres, Commun. Math. Phys. 260 (2005), 203-225. Zbl 1093.58004 MR 2175995
11. Mac Lane, S., Homology, Classics in Mathematics, Springer-Verlag, 1995. Zbl 0818.18001 MR 1344215
12. Neeb, K.-H., Non-abelian extensions of infinite-dimensional Lie-groups, Annales de l'Inst. Fourier 57 (2007), 209-271. Zbl 1127.22008 MR 2316238
13. Neeb, K.-H., On the classification of rational quantum tori and the structure of their automorphism groups, Canadian Mathematical Bulletin 51, (2008), 261-282. Zbl 1163.16014 MR 2414213
14. Schauenburg, P., Hopf-Galois and bi-Galois extensions, Fields Inst. Commun., 43, Amer. Math. Soc., Providence, RI, (2004), 469-515. Zbl 1091.16023 MR 2075600
15. Swan, R. G., Vector bundles and projective modules, Trans. Amer. Math. Soc. 105, (1962), 264-277. Zbl 0109.41601 MR 143225
16. Takai, H., On a Duality for Crossed Products of C∗-Algebras, Journal of Functional Analysis 19, 25-39 (1975). Zbl 0295.46088 MR 365160
17. Tom Dieck, T., Topologie, de Gruyter, 2. Auflage, 2000. Zbl 0966.55001 MR 1150244
18. Wagner, S., Trivial Noncommutative Principal Torus Bundles, Noncommutative Harmonic Analysis with Applications to Probability III, Banach Center Publ. 96 (2012) 299-317. Zbl 1261.46066 MR 2986837
19. Wagner, S., A Geometric Approach to Noncommutative Principal Bundles, PhD Thesis, arXiv:1108.0311v1 [math.DG], 1 Aug 2011.
20. Wagner, S., Free Group Actions from the Viewpoint of Dynamical Systems, Münster J. of Math. 5 (2012), 73-97. Zbl 1286.46076 MR 3047627
21. Wagner, S., A Geometric Approach to Noncommutative Principal Torus Bundles, Proc. London Math. Soc. (3) 106 (2013), no. 6, 1179-1222. Zbl 1277.46039 MR 3072280