来自q-代数的经典动力系统：“簇”变量和显式解
Classical Dynamical Systems from q-algebras:"cluster" variables and explicit solutions
摘要：
通过定义一组适当的集体变量，给出了一种求解具有余代数对称性的N体经典Hamilton系统运动方程显式解的一般方法，这些集体变量是基于余代数生成元上的余积映射的迭代.用这种方法明确地求解了几个由q-Poincare代数得到的N体动力学系统的例子：sl（2）Calogero-Gaudin系统的q-变形版本（q-CG），一个q-Poincare ' Gaudin系统和一个由（1+1）Poincare'代数的相同（非共边界）q-变形产生的Ruijsenaars型系统。同时，给出了所有这些系统作为同一三维可解李群上不同Poisson-Lie动力学的统一解释。
英文摘要：
A general procedure to get the explicit solution of the equations of motion for N-body classical Hamiltonian systems equipped with coalgebra symmetry is introduced by defining a set of appropriate collective variables which are based on the iterations of the coproduct map on the generators of the algebra. In this way several examples of N-body dynamical systems obtained from q-Poisson algebras are explicitly solved: the q-deformed version of the sl(2) Calogero-Gaudin system (q-CG), a q-Poincare' Gaudin system and a system of Ruijsenaars type arising from the same (non co-boundary) q-deformation of the (1+1) Poincare' algebra. Also, a unified interpretation of all these systems as different Poisson-Lie dynamics on the same three dimensional solvable Lie group is given.
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