标题： 手征振荡子的振荡子代数 显示英文标题

标题： Oscillator Algebra of Chiral Oscillator

摘要： 对于由二阶退化拉格朗日描述的具有特殊欧几里得群对称性的手征振荡器，我们通过余切丛哈密顿约化证明，约化后的方程在振荡器代数的对偶上是李-泊松的，这是二维特殊欧几里得代数的中心扩张。此扩张由特殊欧几里得代数的辛二阶循环定义，似乎是对约化本身的加强，这根植于卡西米尔函数。 显示英文摘要

摘要： For the chiral oscillator described by a second order and degenerate Lagrangian with special Euclidean group of symmetries, we show, by cotangent bundle Hamiltonian reduction, that reduced equations are Lie-Poisson on dual of oscillator algebra, the central extension of special Euclidean algebra in two dimensions. This extension, defined by symplectic two-cocycle of special Euclidean algebra, seems to be an enforcement of reduction itself rooted to Casimir function.