Free motion on the Poisson SU(n) group

Abstract

SL(N,C) is the phase space of the Poisson SU(N). We calculate explicitly the symplectic structure of SL(N,C), define an analogue of the Hamiltonian of the free motion on SU(N) and solve the corresponding equations of motion. Velocity is related to the momentum by a non-linear Legendre transformation.

LaTeX, 10 pages

References in corpus (1)

• Phase spaces related to standard classical $r$-matrices

Cited by in corpus (4)

• Poisson-Lie interpretation of trigonometric Ruijsenaars duality
• Poisson-Lie analogues of spin Sutherland models
• Poisson-Lie generalization of the Kazhdan-Kostant-Sternberg reduction
• Reduction of a bi-Hamiltonian hierarchy on $T^{\ast }\mathrm{U}(n)$ to spin Ruijsenaars--Sutherland models