R-matrix brackets and their quantization

J. Donin; D. Gurevich; S. Majid

Annales de l'I.H.P. Physique théorique (1993)

  • Volume: 58, Issue: 2, page 235-246
  • ISSN: 0246-0211

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Donin, J., Gurevich, D., and Majid, S.. "R-matrix brackets and their quantization." Annales de l'I.H.P. Physique théorique 58.2 (1993): 235-246. <http://eudml.org/doc/76604>.

@article{Donin1993,
author = {Donin, J., Gurevich, D., Majid, S.},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {classical -matrix; Poisson brackets; quantization; quantum sphere},
language = {eng},
number = {2},
pages = {235-246},
publisher = {Gauthier-Villars},
title = {R-matrix brackets and their quantization},
url = {http://eudml.org/doc/76604},
volume = {58},
year = {1993},
}

TY - JOUR
AU - Donin, J.
AU - Gurevich, D.
AU - Majid, S.
TI - R-matrix brackets and their quantization
JO - Annales de l'I.H.P. Physique théorique
PY - 1993
PB - Gauthier-Villars
VL - 58
IS - 2
SP - 235
EP - 246
LA - eng
KW - classical -matrix; Poisson brackets; quantization; quantum sphere
UR - http://eudml.org/doc/76604
ER -

References

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  1. [1] A.A. Belavin and V.G. Drinfeld, Triangle Equations and simple Lie Algebras, preprint No. 18, Inst. Theor. Phys. Acad. Sci. U.S.S.R., Chernogolovka, 1982 (in Russian). Zbl0921.58073MR768939
  2. [2] V.G. Drinfeld, On a constant Quasiclassical Solutions of the Yang-Baxter Equations, Sov. Math. Dokl., Vol. 28, 1983, pp. 667-671. Zbl0553.58038
  3. [3] V.G. Drinfeld, Quasi-Hopf Algebras, eng. trans. in Leningrad Math. J., Vol. 1, 1990; pp. 1419-1457, On Quasitriangular Quasi-Hopf Algebras and a Group closely connected with Gal (Q/Q), eng. transl. in Leningrad Math. J., Vol. 2, 1991, pp. 829. Zbl0718.16033MR1047964
  4. [4] I.L. Egusquiza, Quantum Group invariance in Quantum Sphere valued statistical Models, in Phys. Lett. B, Vol. 276, 1992, pp. 465-471. MR1153368
  5. [5] L.D. Faddeev, N. Yu. RESHETIKHIN and L.A. Takhtajan, Quantization of Lie Groups and Lie Algebras, eng. trans. in Leningrad Math. J., Vol. 1, 1990, pp. 193- 225. Zbl0715.17015MR1015339
  6. [6] D.I. Gurevich, V. Rubtsov and N. Zobin, Quantization of Poisson Pairs: the R-Matrix approach, in J. Geom. Phys., Vol. 9, 1992, pp. 25-44. Zbl0747.58058MR1154238
  7. [7] S. Khoroshkin, A. Radul and V. Rubtsov, A family of Poisson structures on compact Hermitian symmetric spaces, preprint IHES/M/91/91. Zbl0785.58024
  8. [8] J.-H. Lu and A. Weinstein, Poisson Lie groups, dressing transformations, and Bruhat decompositions, J. Diff. Geom., Vol. 31, 1990, pp. 501-526. Zbl0673.58018MR1037412
  9. [9] S. Majid, Examples of braided groups and braided matrices, J. Math. Phys., Vol. 32, 1991, pp. 3246-3253. Zbl0821.16042MR1137374
  10. [10] S. Majid, Quasitriangular Hopf algebras and Yang-Baxter equation, Int. J. Modern Physics A, Vol. 5, n° 1, 1990, pp. 1-91 Zbl0709.17009MR1027945
  11. [11] N. Yu. Manin, Quantum groups and non-commutative geometry, Report, Centre de Rech. Math., Montreal, 1988. Zbl0724.17006
  12. [12] P. Podleś, Quantum spheres, Lett. Math. Phys. Vol. 14, 1987, pp. 193-202. Zbl0634.46054MR919322
  13. [13] A. Sheu, J.-H. Lu and A. Weinstein, Quantization of the Poisson SU(2) and its Poisson homogeneous space - the 2-sphere, Comm. Math. Phys., Vol. 135, 1991, pp. 217-232. Zbl0719.58042MR1087382

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