QUADRATIC ALGEBRAS AND INTEGRABLE SYSTEMS

被引:133
作者
FREIDEL, L
MAILLET, JM
机构
[1] LPTHE, Université Pierre et Marie Curie, F-75252 Paris
关键词
D O I
10.1016/0370-2693(91)91566-E
中图分类号
P1 [天文学];
学科分类号
0704 ;
摘要
We present new classical and quantum quadratic algebras that generalize the usual R-matrix and quantum group structures of integrable systems. In their classical and infinitesimal limit, they correspond to Lie-Poisson brackets defined by a non-skew-symmetric R-matrices solution of the classical Yang-Baxter equation.
引用
收藏
页码:278 / 284
页数:7
相关论文
共 18 条
[1]   POISSON STRUCTURE AND INTEGRABILITY OF THE NEUMANN-MOSER-UHLENBECK MODEL [J].
AVAN, J ;
TALON, M .
INTERNATIONAL JOURNAL OF MODERN PHYSICS A, 1990, 5 (23) :4477-4488
[2]  
Baxter R.J., 2007, EXACTLY SOLVED MODEL
[3]  
DRINFELD VG, 1983, DOKL AKAD NAUK SSSR+, V268, P285
[4]  
Faddeev L.D., 1988, ALGEBRAIC ANAL, VI, P129
[5]   QUANTUM R-MATRIX FOR THE GENERALIZED TODA SYSTEM [J].
JIMBO, M .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1986, 102 (04) :537-547
[6]   KAC-MOODY ALGEBRA AND EXTENDED YANG-BAXTER RELATIONS IN THE O(N) NON-LINEAR SIGMA-MODEL [J].
MAILLET, JM .
PHYSICS LETTERS B, 1985, 162 (1-3) :137-142
[7]   NEW INTEGRABLE CANONICAL STRUCTURES IN TWO-DIMENSIONAL MODELS [J].
MAILLET, JM .
NUCLEAR PHYSICS B, 1986, 269 (01) :54-76
[8]   HAMILTONIAN STRUCTURES FOR INTEGRABLE CLASSICAL-THEORIES FROM GRADED KAC-MOODY ALGEBRAS [J].
MAILLET, JM .
PHYSICS LETTERS B, 1986, 167 (04) :401-405
[9]   LAX EQUATIONS AND QUANTUM GROUPS [J].
MAILLET, JM .
PHYSICS LETTERS B, 1990, 245 (3-4) :480-486
[10]   DRESSING TRANSFORMATIONS AND POISSON GROUP-ACTIONS [J].
SEMENOVTIANSHANSKY, MA .
PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES, 1985, 21 (06) :1237-1260