If G is a Lie group, the differential of each inner automorphism determines a linear transformation on the tangent space to G at the identity element, because the identity is fixed by any inner automorphism. This gives rise to a linear representation of the group G in the Lie algebra G of...
3) adjoint group of a Lie group 李群伴随群4) adjoint satellite cluster 伴随卫星群 1. Orbit design for the space station adjoint satellite cluster considering the impact of perturbation; 考虑摄动影响的空间站伴随卫星群轨道设计5) adjoint semigroups 伴随有半群...
Lie groupsHamiltonian systemsVariational principlesAdjoint systemsWe present a novel Type II variational principle on the cotangent bundle of a Lie group which enforces Type II boundary conditions, i.e., fixed initial position and final momentum. In general, such Type II variational principles are ...
Homotopy Theory of Lie Groups-Chapter 19 This chapter discusses the homotopy theory of lie groups. M.S. Lie created the notion of Lie group, then called it a topological group. One of the motivati... M Mimura - 《Handbook of Algebraic Topology》 被引量: 89发表: 1995年 ...
5) adjoint group of an algebraic group 代数群的伴随群 6) adjoint group of a Lie group 李群伴随群 补充资料:代数的代数 代数的代数 algebraic algebra 代数的代数【aigeb面c aigeb口;缸代6脚盼贬军粗,即;浦钾! 域F上幂结合代数洲特别地结合代数飞.其所有兀素都是代数的几素a任月称为代数的(al罗...
A Poisson-Lie group acting by the coadjoint action on the dual of its Lie algebra induces on it a non-trivial class of quadratic Poisson structures extending the linear Poisson bracket on the coadjoint orbits.doi:10.2991/jnmp.1999.6.3.9Kupershmidt, Boris A....
This study is based on the Lie group method for the nonlinear elastic structural element equation (ESE Equation). We obtain a three-dimensional Lie algebra. By utilizing this Lie algebra a four-dimensional optimal system is constructed. The governing ESE Equation is converted to nonlinear ordinary...
1.The adjoint representations of Hopf algebras with non-degenerate Killing formKilling根非退化下Hopf代数的伴随表示 2.In this paper,some properties of Lie Group and the adjoint representation of Lie Group are discussed.本文讨论了李群及李群伴随表示不变子空间的性质,文末对李群还引入了一种联络。 3.In...
The purpose of this article is to study in detail the actions of a semisimple Lie or algebraic group on its Lie algebra by the adjoint representation and on itself by the adjoint action. We will focus primarily on orbits through nilpotent elements in the Lie algebra; these are called nilpoten...
In this chapter we prove, among other things, that the coadjoint orbits of a Lie group are symplectic manifolds. These symplectic manifolds are, in fact, the symplectic leaves for the Lie-Poisson bracket. This result was developed and used by Kirillov, Arnold, Kostant, and Souriau in the ...