Some remarks on quantum and braided group gauge theory

Shahn Majid

Banach Center Publications (1997)

  • Volume: 40, Issue: 1, page 335-349
  • ISSN: 0137-6934

Abstract

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We clarify some aspects of quantum group gauge theory and its recent generalisations (by T. Brzeziński and the author) to braided group gauge theory and coalgebra gauge theory. We outline the diagrammatic version of the braided case. The bosonisation of any braided group provides us a trivial principal bundle in three ways.

How to cite

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Majid, Shahn. "Some remarks on quantum and braided group gauge theory." Banach Center Publications 40.1 (1997): 335-349. <http://eudml.org/doc/252224>.

@article{Majid1997,
abstract = {We clarify some aspects of quantum group gauge theory and its recent generalisations (by T. Brzeziński and the author) to braided group gauge theory and coalgebra gauge theory. We outline the diagrammatic version of the braided case. The bosonisation of any braided group provides us a trivial principal bundle in three ways.},
author = {Majid, Shahn},
journal = {Banach Center Publications},
keywords = {bosonisation; gauge theory; connection; braided group; quantum group; fiber bundle; noncommutative geometry; fibre bundle; principal bundle},
language = {eng},
number = {1},
pages = {335-349},
title = {Some remarks on quantum and braided group gauge theory},
url = {http://eudml.org/doc/252224},
volume = {40},
year = {1997},
}

TY - JOUR
AU - Majid, Shahn
TI - Some remarks on quantum and braided group gauge theory
JO - Banach Center Publications
PY - 1997
VL - 40
IS - 1
SP - 335
EP - 349
AB - We clarify some aspects of quantum group gauge theory and its recent generalisations (by T. Brzeziński and the author) to braided group gauge theory and coalgebra gauge theory. We outline the diagrammatic version of the braided case. The bosonisation of any braided group provides us a trivial principal bundle in three ways.
LA - eng
KW - bosonisation; gauge theory; connection; braided group; quantum group; fiber bundle; noncommutative geometry; fibre bundle; principal bundle
UR - http://eudml.org/doc/252224
ER -

References

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  1. [1] T. Brzeziński and S. Majid, Quantum group gauge theory on quantum spaces. Commun. Math. Phys., 157:591-638, 1993. Erratum 167:235, 1995. Zbl0817.58003
  2. [2] T. Brzeziński and S. Majid, Quantum group gauge theory and Q-monopoles. In M. Olmo et al, editor, Anales de Física Monografías, volume 1, pages 75-78. CIEMAT/RSEF, Madrid, 1993. 
  3. [3] T. Brzeziński, Translation map in quantum principal bundles. J. Geom. Phys., 20:347-368, 1996. Zbl0867.55015
  4. [4] P. Hajac, Strong connections on quantum principal bundles. Commun. Math. Phys., To appear, 1997. Zbl0873.58007
  5. [5] T. Brzeziński and S. Majid, Coalgebra gauge theory. Preprint, Damtp/95-74, 1995. 
  6. [6] T. Brzeziński, Quantum homogeneous spaces as quantum quotient spaces. J. Math. Phys., 37:2388-2399, 1996. Zbl0878.17011
  7. [7] S. Majid, Diagrammatics of braided group gauge theory. Preprint, Damtp/96-31, 1996. 
  8. [8] S. Majid, Braided momentum in the q-Poincaré group. J. Math. Phys., 34:2045-2058, 1993. Zbl0786.17013
  9. [9] S. Majid, Foundations of Quantum Group Theory. Cambridge Univeristy Press, 1995. Zbl0857.17009
  10. [10] S. Majid, Cross product quantization, nonabelian cohomology and twisting of Hopf algebras. In V.K. Dobrev, H.-D. Doebner and A.G. Ushveridze, editors, Generalised Symmetries in Physics, pages 13-41. World Sci., 1994. 
  11. [11] Y. Doi, Equivalent crossed products for a Hopf algebra. Commun. Algebra, 17:3053-3085, 1989. Zbl0687.16008
  12. [12] S. Majid, Examples of braided groups and braided matrices. J. Math. Phys., 32:3246-3253, 1991. Zbl0821.16042
  13. [13] S. Majid, Quantum and braided linear algebra. J. Math. Phys., 34:1176-1196, 1993. Zbl0781.17005
  14. [14] S. Majid, Beyond supersymmetry and quantum symmetry (an introduction to braided groups and braided matrices). In M-L. Ge and H.J. de Vega, editors, Quantum Groups, Integrable Statistical Models and Knot Theory, pages 231-282. World Sci., 1993. 
  15. [15] S. Majid, Braided groups and algebraic quantum field theories. Lett. Math. Phys., 22:167-176, 1991. Zbl0745.16019
  16. [16] S. Majid, Cross products by braided groups and bosonization. J. Algebra, 163:165-190, 1994. Zbl0807.16036
  17. [17] S. Majid, Quantum and braided Lie algebras. J. Geom. Phys., 13:307-356, 1994. Zbl0821.17007
  18. [18] S. Majid, Quasi-* structure on q-Poincaré algebras. J. Geom. Phys., To appear, 1997. Zbl0882.16025

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