SOME POISSON STRUCTURES ASSOCIATED TO DRINFELD-JIMBO R-MATRICES AND THEIR QUANTIZATION

被引：8

作者：

DONIN, J ^{[1
]}

GUREVICH, D ^{[1
]}

机构：

[1] MAX PLANCK INST MATH,W-5300 BONN 3,GERMANY

来源：

ISRAEL JOURNAL OF MATHEMATICS | 1995年 / 92卷 / 1-3期

关键词：

D O I：

10.1007/BF02762068

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We describe various ways of constructing Poisson structures associated to Drinfeld-Jimbo R-matrices on homogeneous spaces, research some relations between these structures, and quantize some oi them.

引用

页码：23 / 32

页数：10

共 10 条

[1]

Donin J., Gurevich D., Quasi-Hopf algebras and R-matrix structure in line bundles over flag manifolds, Selecta Mathematica Formerly Sovietica, 12, pp. 37-48, (1993)

[2]

Donin J., Gurevich D., Majid S., R-matrix brackets and their quantization, Annales de l’Institut Henri Poincaré. Physique Théorique, 58, pp. 235-246, (1993)

[3]

Drinfeld V.G., Quantum groups, pp. 798-820, (1986)

[4]

Drinfeld V., On almost cocommutative Hopf algebras, Leningrad Mathematical Journal, 1, 2, pp. 321-342, (1990)

[5]

Drinfeld V., Quasi-Hopf algebra, Leningrad Mathematical Journal, 1, 6, pp. 1419-1457, (1990)

[6]

Gurevich D., Rubtsov V., Zobin N., Quantization of Poisson pairs: R-matrix approach, Journal of Geometry and Physics, 9, pp. 25-44, (1992)

[7]

Helgason S., Differential Geometry, Lie Groups, and Symmetric Spaces, (1978)

[8]

Khoroshkin S., Radul A., Rubtsov V., A family of Poisson structures on compact Hermitian symmetric spaces, Communications in Mathematical Physics, 152, pp. 299-316, (1993)

[9]

Lu J.H., Weinstein A., Poisson Lie groups, dressing transformations, and Bruhat decompositions, Journal of Differential Geometry, 31, pp. 501-526, (1990)

[10]

Takhtajan L., Introduction to quantum groups, pp. 3-28, (1990)

← 1 →