Semidirect product reduction theory: a user's guide

一种计算半直积约化导出的2-上循环的简便方法

An easier way to compute 2-cocycles coming from a reduction for semidirect products

本文针对半直积哈密顿作用中由剩余作用产生的2-上循环问题，受带边曲面泰希米勒空间上Virasoro代数哈密顿作用研究启发，建立一般框架并提出了获取对应Gelfand-Fuchs 2-上循环的简便方法。

The Landau-Lifshitz Equation by Semidirect Product Reduction

The Landau-Lifshitz equation is derived as the reduction of a geodesic flow on the group of maps into the rotation group. Passing the symmetries of spatial isotropy to the reduced space is an example of semidirect product reduction by stages.

Dirac Reduction for Nonholonomic Mechanical Systems and Semidirect Products

This paper develops the theory of Dirac reduction by symmetry for nonholonomic systems on Lie groups with broken symmetry. The reduction is carried out for the Dirac structures, as well as for the associated Lagrange-Dirac and Hamilton-Dirac dynamical systems. This reduction procedure is accompanied by reduction of the associated variational structures on both Lagrangian and Hamiltonian sides. The reduced dynamical systems obtained are called the implicit Euler-Poincaré-Suslov equations with advected parameters and the implicit Lie-Poisson-Suslov equations with advected parameters. The theory …

Discrete Lagrangian reduction, discrete Euler-Poincare equations, and semidirect products

A discrete version of Lagrangian reduction is developed in the context of discrete time Lagrangian systems on $G\times G$, where $G$ is a Lie group. We consider the case when the Lagrange function is invariant with respect to the action of an isotropy subgroup of a fixed element in the representation space of $G$. In this context the reduction of the discrete Euler-Lagrange equations is shown to lead to the so called discrete Euler-Poincaré equations. A constrained variational principle is derived. The Legendre transformation of the discrete Euler-Poincaré equations leads to discrete Hamiltoni…

中心半直积上场论的协变Euler-Poincaré约化

Covariant Euler-Poincaré Reduction for Field Theories on Centered Semidirect Products

本文针对中心半直积主丛上的协变场论，从拉格朗日与哈密顿视角建立约化方案，得到分解的Euler-Poincaré与Lie-Poisson方程、多辛公式及守恒律，并应用于矩阵微结构与jet群模型，验证了理论的有效性。

Lindblad量子动力学作为伴随耦合半直接积上的Euler-Poincaré约简

Lindblad Quantum Dynamics as Euler-Poincaré Reduction on Adjoint-Coupled Semidirect Products

本文通过几何方法推导Lindblad方程，揭示其作为Euler-Poincaré约简中的曲率诱导收缩，展现其在SU(n)群作用下的结构和应用。