Communications in Mathematical Physics

, Volume 168, Issue 2, pp 249–264 | Cite as

q-Lorentz group and braided coaddition onq-Minkowski space

  • Ulrich Meyer
Article

Abstract

We present a new version ofq-Minkowski space, which has both a coaddition law and anSLq(2, ℂ) decomposition. The additive structure forms a braided group rather than a quantum one. In the process, we obtain aq-Lorentz group which coacts covariantly on thisq-Minkowski space.

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References

  1. 1.
    Abe, E.: Hopf Algebras. Cambridge: Cambridge University Press, 1980Google Scholar
  2. 2.
    Carow-Watamura, U., Schlieker, M., Scholl, M., Watamura, S.: A quantum Lorentz group. Int. J. Mod. Phys.A (17), 3081–3108 (1991)Google Scholar
  3. 3.
    Connes, A.: Géométrie non commutative. InterEditions, 1990Google Scholar
  4. 4.
    Drinfel'd, V.G.: Quantum groups. Proceedings of the ICM, 1986, pp. 798–820Google Scholar
  5. 5.
    Jimbo, M.: Aq-difference analogue of U(g) and the Yang-Baxter equation. Lett. Math. Phys.10, 63–69 (1985)Google Scholar
  6. 6.
    Majid, S.: More examples of bicrossproduct and double cross product Hopf algebras. Isr. J. Math.722(1–2), 133–148 (1990)Google Scholar
  7. 7.
    Majid, S.: Onq-regularization. Int. J. Mod. Phys.A(5), 4689–4696 (1990)Google Scholar
  8. 8.
    Majid, S.: Quasitriangular Hopf algebras and Yang-Baxter equations. Int. J. Mod. Phys.A(5), 1–91 (1990)Google Scholar
  9. 9.
    Majid, S.: Braided groups and algebraic quantum field theories. Lett. Math. Phys.22, 167–175 (1991)Google Scholar
  10. 10.
    Majid, S.: Examples of braided groups and braided matrices. J. Math. Phys.32, 3246–3253 (1991)Google Scholar
  11. 11.
    Majid, S.: Rank of quantum groups and braided groups in dual form. In: Kulish, P.P. (ed.) Quantum Groups. Proceedings, Leningrad 1990, Berlin Heidelberg. New York: Springer 1992, pp. 79–89Google Scholar
  12. 12.
    Majid, S.: Braided groups. J. Pure Applied Algebra86, 187–221 (1993)Google Scholar
  13. 13.
    Majid, S.: Braided momentum in theq-Poincaré group. J. Math. Phys.34 2045–2058 (1993)Google Scholar
  14. 14.
    Majid, S.: Quantum and braided linear algebra. J. Math. Phys.34, 1176–1196 (1993)Google Scholar
  15. 15.
    Majid, S.: The quantum double as quantum mechanics. J. Geom. Phys.13, 169–202 (1994)Google Scholar
  16. 16.
    Ogievetsky, O., Schmidke, W.B., Wess, J., Zumino, B.:q-Deformed Poincaré algebra. Commun. Math. Phys.150, 495–518 (1992)Google Scholar
  17. 17.
    Podleś, P., Woronowicz, S.L.: Quantum deformation of Lorentz group. Commun. Math. Phys.130, 381–431 (1990)Google Scholar
  18. 18.
    Reshetikhin, N.Yu., Takhtadzhyan, L.A., Faddeev, L.D.: Quantization of Lie groups and Lie algebras. Leningrad Math. J.1(1), 193–225 (1990)Google Scholar
  19. 19.
    Reshetikin, N.Yu., Semenov-Tian-Shansky, M.A.: Quantum R-matrices and factorization problems. Leningrad Math. J.1(1), (1990)Google Scholar
  20. 20.
    Schlieker, M., Weich, W., Weixler, R.: Inhomogeneous quantum groups. Z. Phys. C,53, 79–82 (1992)Google Scholar
  21. 21.
    Sweedler, M.E.: Hopf Algebras. New York: Benjamin, W.A., 1969Google Scholar
  22. 22.
    Woronowicz, S.L.: Compact matrix pseudogroups. Commun. Math. Phys.111, 613–665 (1987)Google Scholar

Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • Ulrich Meyer
    • 1
  1. 1.Department of Applied Mathematics and Theoretical PhysicsUniversity of CambridgeCambridgeEngland

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