Quantum Fibre Bundles. An Introduction
Brzeziński, Tomasz
Banach Center Publications, Tome 38 (1997), p. 211-223 / Harvested from The Polish Digital Mathematics Library
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An approach to construction of a quantum group gauge theory based on the quantum group generalisation of fibre bundles is reviewed.

Publié le : 1997-01-01
EUDML-ID : urn:eudml:doc:208664 
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     author = {Brzezi\'nski, Tomasz},
     title = {Quantum Fibre Bundles. An Introduction},
     journal = {Banach Center Publications},
     volume = {38},
     year = {1997},
     pages = {211-223},
     zbl = {0885.58007},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv39z1p211bwm}
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Brzeziński, Tomasz. Quantum Fibre Bundles. An Introduction. Banach Center Publications, Tome 38 (1997) pp. 211-223. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv39z1p211bwm/

[000] [1] R. J. Blattner, M. Cohen and S. Montgomery, Crossed Products and Inner Actions of Hopf Algebras, Trans. Amer. Math. Soc. 298 (1986), 671. | Zbl 0619.16004

[001] [2] R. J. Blattner and S. Montgomery, Crossed Products and Galois Extensions of Hopf Algebras, Pacific J. Math. 137 (1989), 37. | Zbl 0675.16017

[002] [3] T. Brzeziński, Differential Geometry of Quantum Groups and Quantum Fibre Bundles, University of Cambridge, Ph.D. thesis, 1994.

[003] [4] T. Brzeziński, Remarks on Quantum Principal Bundles, in: Quantum Groups. Formalism and Applications, J. Lukierski, Z. Popowicz and J. Sobczyk, eds. Polish Scientific Publishers PWN, 1995, p. 3. | Zbl 0877.58004

[004] [5] T. Brzeziński, Translation Map in Quantum Principal Bundles, preprint (1994) hep-th/9407145, J. Geom. Phys. to appear.

[005] [6] T. Brzeziński, Quantum Homogeneous Spaces as Quantum Quotient Spaces, preprint (1995) q-alg/9509015. | Zbl 0878.17011

[006] [7] T. Brzeziński and S. Majid, Quantum Group Gauge Theory on Quantum Spaces, Comm. Math. Phys. 157 (1993), 591; ibid. 167 (1995), 235 (erratum). | Zbl 0817.58003

[007] [8] T. Brzeziński and S. Majid, Quantum Group Gauge Theory on Classical Spaces, Phys. Lett. B 298 (1993), 339. | Zbl 0817.58003

[008] [9] T. Brzeziński and S. Majid, Coalgebra Gauge Theory, Preprint DAMTP/95-74, 1995.

[009] [10] R. J. Budzyński and W. Kondracki, Quantum principal fiber bundles: topological aspects, preprint (1994) hep-th/9401019.

[010] [11] C.-S. Chu, P.-M. Ho and H. Steinacker, Q-deformed Dirac monopole with arbitrary charge, preprint (1994) hep-th/9404023.

[011] [12] A. Connes, Non-Commutative Geometry, Academic Press, 1994.

[012] [13] A. Connes, A lecture given at the Conference on Non-commutative Geometry and Its Applications, Castle Třešť, Czech Republic, May 1995.

[013] [14] A. Connes and M. Rieffel, Yang-Mills for Non-Commutative Two-Tori, Contemp. Math. 62 (1987), 237.

[014] [15] Y. Doi, Equivalent Crossed Products for a Hopf Algebra, Comm. Algebra 17 (1989), 3053. | Zbl 0687.16008

[015] [16] Y. Doi and M. Takeuchi, Cleft Module Algebras and Hopf Modules, Comm. Algebra 14 (1986), 801. | Zbl 0589.16011

[016] [17] V. G. Drinfeld, Quantum Groups, in: Proceedings of the International Congress of Mathematicians, Berkeley, California, Vol. 1, Academic Press, 1986, p. 798.

[017] [18] T. Eguchi, P. Gilkey and A. Hanson, Gravitation, Gauge Theories and Differential Geometry, Phys. Rep. 66 (1980), 213.

[018] [19] P. M. Hajac, Strong Connections and Uq(2)-Yang-Mills Theory on Quantum Principal Bundles, preprint (1994) hep-th/9406129.

[019] [20] D. Husemoller, Fibre Bundles, Springer-Verlag, 3rd ed. 1994.

[020] [21] D. Kastler, Cyclic Cohomology within Differential Envelope, Hermann, 1988. | Zbl 0662.55001

[021] [22] E. Kunz, Kähler Differentials, Vieweg & Sohn, 1986.

[022] [23] S. Majid, Cross Product Quantisation, Nonabelian Cohomology and Twisting of Hopf Algebras, in: Generalised Symmetries in Physics, H.-D. Doebner, V. K. Dobrev and A. G. Ushveridze, eds., World Scientific, 1994, p. 13.

[023] [24] U. Meyer, Projective Quantum Spaces, Lett. Math. Phys. 35 (1995), 91.

[024] [25] M. Pflaum, Quantum Groups on Fibre Bundles, Comm. Math. Phys. 166 (1994), 279. | Zbl 0824.58009

[025] [26] P. Podleś, Quantum Spheres, Lett. Math. Phys. 14 (1987), 193.

[026] [27] H.-J. Schneider, Principal Homogeneous Spaces for Arbitrary Hopf Algebras, Israel J. Math. 72 (1990), 167. | Zbl 0731.16027

[027] [28] M. E. Sweedler, Hopf Algebras, Benjamin, 1969.

[028] [29] M. E. Sweedler, Cohomology of Algebras over Hopf Algebras, Trans. Amer. Math. Soc. 133 (1968), 205.

[029] [30] S. L. Woronowicz, Twisted SU2 Group. An Example of a Non-commutative Differential Calculus, Publ. Res. Inst. Math. Sci. 23 (1987), 117.

[030] [31] S. L. Woronowicz, Differential Calculus on Compact Matrix Pseudogroups (Quantum Groups), Comm. Math. Phys. 122 (1989), 125. | Zbl 0751.58042