Quantum deformations of the Lorentz group. The Hopf-algebra level

S. L. Woronowicz; S. Zakrzewski

Compositio Mathematica (1994)

  • Volume: 90, Issue: 2, page 211-243
  • ISSN: 0010-437X

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Woronowicz, S. L., and Zakrzewski, S.. "Quantum deformations of the Lorentz group. The Hopf-algebra level." Compositio Mathematica 90.2 (1994): 211-243. <http://eudml.org/doc/90273>.

@article{Woronowicz1994,
author = {Woronowicz, S. L., Zakrzewski, S.},
journal = {Compositio Mathematica},
keywords = {Hopf -algebra; 2-dimensional corepresentation; quantum Lorentz groups; Poisson-Lie structures},
language = {eng},
number = {2},
pages = {211-243},
publisher = {Kluwer Academic Publishers},
title = {Quantum deformations of the Lorentz group. The Hopf-algebra level},
url = {http://eudml.org/doc/90273},
volume = {90},
year = {1994},
}

TY - JOUR
AU - Woronowicz, S. L.
AU - Zakrzewski, S.
TI - Quantum deformations of the Lorentz group. The Hopf-algebra level
JO - Compositio Mathematica
PY - 1994
PB - Kluwer Academic Publishers
VL - 90
IS - 2
SP - 211
EP - 243
LA - eng
KW - Hopf -algebra; 2-dimensional corepresentation; quantum Lorentz groups; Poisson-Lie structures
UR - http://eudml.org/doc/90273
ER -

References

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  1. [1] Podleś, P. and Woronowicz, S.L.: Quantum deformation of Lorentz group, Commun. Math. Phys.130 (1990) 381-431. Zbl0703.22018MR1059324
  2. [2] Woronowicz, S.L. and Zakrzewski, S.: Quantum Lorentz group having Gauss decomposition property, Publ. R.I.M.S., Kyoto University28 (1992) 809-824. Zbl0811.17012MR1196000
  3. [3] Drinfeld, V.G.: Quantum Groups, pp. 798-820 in Proceeding of the ICM, Berkeley, 1986, AMS 1987. Zbl0667.16003MR934283
  4. [4] Sojbelman, J.S.: Irreducible representations of the algebra of functions on the quantum SU(N) group and Schubert cells, Dokl. Akad. Nauk. SSSR307 (1989) 41-45 (in Russian). Zbl0698.22015
  5. [5] Faddeev, L.D., Reshethikin, N. Yu., and Takhtajan, L.A.: Quantization of Lie groups and Lie algebras, Algebra i analiz1 (1989) 178-206 (in Russian). Zbl0715.17015MR1015339
  6. [6] Manin, Yu. I.: Quantum groups and non-commutative geometry, Pub. C.R.M.Montréal (1988). Zbl0724.17006MR1016381
  7. [7] Manin, Yu. I.:Leçons Collége de France (1989). 
  8. [8] Dubois-Violette, M. and Launer, G.: The quantum group of a non-degenerate bilinear form, Physics LettersB, Vol. 245, No. 2 (1990) 175-177. Zbl1119.16307MR1068703
  9. [9] Podleś, P.: Complex quantum groups and their real representations, Publ. R.I.M.S., Kyoto University28 (1992) 709-745. Zbl0809.17003MR1195996
  10. [10] Woronowicz, S.L.: Compact matrix pseudogroups, Commun. Math. Phys.111 (1987) 613-665. Zbl0627.58034MR901157
  11. [11] Woronowicz, S.L.: New deformation of SL(2, C). Hopf-algebra level, Rep. Math. Phys.30 No. 2 (1991) 259-269. Zbl0759.17010
  12. [12] Zakrzewski, S.: Hopf *-algebra of polynomials on the quantum SL(2, R) for a "unitary" R-matrix, Lett. Math. Phys.22 (1991) 287-289. Zbl0752.17018MR1131752
  13. [13] Zakrzewski, S.: Realifications of complex quantum groups, in Groups and related topics, R. Gielerak et al. (eds.), Kluwer1992, 83-100. Zbl0834.17010MR1205603
  14. [14] Zakrzewski, S.: Poisson structures on the Lorentz group, preprint, Warsaw, March 1993. Zbl0827.17016

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