Quantum Fibre Bundles. An Introduction

• Autorzy: Tomasz Brzeziński
• Języki publikacji: EN

Abstrakty

EN

An approach to construction of a quantum group gauge theory based on the quantum group generalisation of fibre bundles is reviewed.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 1997
• Tom: 39
• Numer: 1
• Strony: 211-223

Daty

wydano

1997

Twórcy

autor

Tomasz Brzeziński

• Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 9EW, U.K.

Bibliografia

• [1] R. J. Blattner, M. Cohen and S. Montgomery, Crossed Products and Inner Actions of Hopf Algebras, Trans. Amer. Math. Soc. 298 (1986), 671.
• [2] R. J. Blattner and S. Montgomery, Crossed Products and Galois Extensions of Hopf Algebras, Pacific J. Math. 137 (1989), 37.
• [3] T. Brzeziński, Differential Geometry of Quantum Groups and Quantum Fibre Bundles, University of Cambridge, Ph.D. thesis, 1994.
• [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.
• [5] T. Brzeziński, Translation Map in Quantum Principal Bundles, preprint (1994) hep-th/9407145, J. Geom. Phys. to appear.
• [6] T. Brzeziński, Quantum Homogeneous Spaces as Quantum Quotient Spaces, preprint (1995) q-alg/9509015.
• [7] T. Brzeziński and S. Majid, Quantum Group Gauge Theory on Quantum Spaces, Comm. Math. Phys. 157 (1993), 591; ibid. 167 (1995), 235 (erratum).
• [8] T. Brzeziński and S. Majid, Quantum Group Gauge Theory on Classical Spaces, Phys. Lett. B 298 (1993), 339.
• [9] T. Brzeziński and S. Majid, Coalgebra Gauge Theory, Preprint DAMTP/95-74, 1995.
• [10] R. J. Budzyński and W. Kondracki, Quantum principal fiber bundles: topological aspects, preprint (1994) hep-th/9401019.
• [11] C.-S. Chu, P.-M. Ho and H. Steinacker, Q-deformed Dirac monopole with arbitrary charge, preprint (1994) hep-th/9404023.
• [12] A. Connes, Non-Commutative Geometry, Academic Press, 1994.
• [13] A. Connes, A lecture given at the Conference on Non-commutative Geometry and Its Applications, Castle Třešť, Czech Republic, May 1995.
• [14] A. Connes and M. Rieffel, Yang-Mills for Non-Commutative Two-Tori, Contemp. Math. 62 (1987), 237.
• [15] Y. Doi, Equivalent Crossed Products for a Hopf Algebra, Comm. Algebra 17 (1989), 3053.
• [16] Y. Doi and M. Takeuchi, Cleft Module Algebras and Hopf Modules, Comm. Algebra 14 (1986), 801.
• [17] V. G. Drinfeld, Quantum Groups, in: Proceedings of the International Congress of Mathematicians, Berkeley, California, Vol. 1, Academic Press, 1986, p. 798.
• [18] T. Eguchi, P. Gilkey and A. Hanson, Gravitation, Gauge Theories and Differential Geometry, Phys. Rep. 66 (1980), 213.
• [19] P. M. Hajac, Strong Connections and $U \sb q(2)$-Yang-Mills Theory on Quantum Principal Bundles, preprint (1994) hep-th/9406129.
• [20] D. Husemoller, Fibre Bundles, Springer-Verlag, 3rd ed. 1994.
• [21] D. Kastler, Cyclic Cohomology within Differential Envelope, Hermann, 1988.
• [22] E. Kunz, Kähler Differentials, Vieweg & Sohn, 1986.
• [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.
• [24] U. Meyer, Projective Quantum Spaces, Lett. Math. Phys. 35 (1995), 91.
• [25] M. Pflaum, Quantum Groups on Fibre Bundles, Comm. Math. Phys. 166 (1994), 279.
• [26] P. Podleś, Quantum Spheres, Lett. Math. Phys. 14 (1987), 193.
• [27] H.-J. Schneider, Principal Homogeneous Spaces for Arbitrary Hopf Algebras, Israel J. Math. 72 (1990), 167.
• [28] M. E. Sweedler, Hopf Algebras, Benjamin, 1969.
• [29] M. E. Sweedler, Cohomology of Algebras over Hopf Algebras, Trans. Amer. Math. Soc. 133 (1968), 205.
• [30] S. L. Woronowicz, Twisted $SU \sb 2$ Group. An Example of a Non-commutative Differential Calculus, Publ. Res. Inst. Math. Sci. 23 (1987), 117.
• [31] S. L. Woronowicz, Differential Calculus on Compact Matrix Pseudogroups (Quantum Groups), Comm. Math. Phys. 122 (1989), 125.