SYMPLECTIC STRUCTURES ASSOCIATED TO LIE-POISSON GROUPS

被引：123

作者：

ALEKSEEV, AY ^{[1
]}

MALKIN, AZ ^{[1
]}

机构：

[1] UPPSALA UNIV,INST THEORET PHYS,S-75108 UPPSALA,SWEDEN

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 1994年 / 162卷 / 01期

关键词：

D O I：

10.1007/BF02105190

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

The Lie-Poisson analogues of the cotangent bundle and coadjoint orbits of a Lie group are considered. For the natural Poisson brackets the symplectic leaves in these manifolds are classified and the corresponding symplectic forms are described. Thus the construction of the Kirillov symplectic form is generalized for Lie-Poisson groups.

引用

页码：147 / 173

页数：27

共 50 条

[1] Deformed Lie-Poisson structures for quantized groups
Lyakhovsky, VD
Mirolubov, AM
CZECHOSLOVAK JOURNAL OF PHYSICS, 1997, 47 (01) : 63 - 70
[2] LIE-POISSON GROUPS - REMARKS AND EXAMPLES
CAHEN, M
GUTT, S
OHN, C
PARKER, M
LETTERS IN MATHEMATICAL PHYSICS, 1990, 19 (04) : 343 - 353
[3] Symplectic leaves in real Banach Lie-Poisson spaces
Beltita, D
Ratiu, TS
GEOMETRIC AND FUNCTIONAL ANALYSIS, 2005, 15 (04) : 753 - 779
[4] Triangular Poisson structures on Lie groups and symplectic reduction
Hodges, TJ
Yakimov, M
Noncommutative Geometry and Representation Theory in Mathematical Physics, 2005, 391 : 123 - 134
[5] Contractions in deformed Lie-Poisson structures
Lyakhovsky, VD
Mirolyubov, AM
INTERNATIONAL JOURNAL OF MODERN PHYSICS A, 1997, 12 (01): : 225 - 230
[6] Quadratic deformations of Lie-Poisson structures
Lin, Qian
Liu, Zhangju
Sheng, Yunhe
LETTERS IN MATHEMATICAL PHYSICS, 2008, 83 (03) : 217 - 229
[7] DYNAMICAL ASPECTS OF LIE-POISSON STRUCTURES
LIZZI, F
MARMO, G
SPARANO, G
VITALE, P
MODERN PHYSICS LETTERS A, 1993, 8 (31) : 2973 - 2987
[8] LIE-POISSON STRUCTURES OVER DIFFERENTIAL ALGEBRAS
Zharinov, V. V.
THEORETICAL AND MATHEMATICAL PHYSICS, 2017, 192 (03) : 1337 - 1349
[9] Quantization of Lie-Poisson structures by peripheric chains
Lyakhovsky, VD
del Olmo, MA
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2002, 35 (27): : 5731 - 5750
[10] Poisson integrators for Lie-Poisson structures on R3
Song, Lina
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2011, 44 (15)

← 1 2 3 4 5 →