In this chapter, we explain why the orbit of the adjoint action on the Lie algebra of a Lie group is symplectic, and define its symplectic form (the Kirillov–Kostant–Souriau form). An example of an...doi:10.1007/978-3-030-27227-2_5Dwivedi, Shubham...
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...
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....
The arguments are based on auxiliary results on subgroups of free products with central amalgamation.Key Words: Adjoint action,Adjoint representation,Amalgamated product,Center,Direct limit,Normal subgroup,p-Adic Lie group,Radical,Solubility2010 Mathematics Subject Classification: Primary: 22E20,Secondary: ...
摘要: Homotopy normality of Lie groups is studied by using the adjoint action on the space of based loops.关键词: Homotopy normality of Lie groups and the adjoint action, Artículo DOI: 10.1006/jmaa.1995.1057 被引量: 77 年份: 2003
The article discusses the properties of the adjoint action of the complex form of a compact semisimple Lie group on its Lie algebra. The author states that the adjoint orbits of a compact Lie group are K盲hler manifolds and it is natural to expect that complexification of the action will ...
1.Killing form and Adjoint Representations of Hopf Algebras;Hopf代数的Killing型与伴随表示 2.The adjoint representations of Hopf algebras with non-degenerate Killing formKilling根非退化下Hopf代数的伴随表示 3.Representation and Adjoint Action of Quantum Algebra U_q(f(K, (?)));量子代数U_q(f(K,(...
73 of the Lie bracket in the Lie algebra. So for the adjoint action, the infinitesimal generator corresponding to ξ is taking the Lie bracket: η ↠ [ξ,η]. To sum up: eq. 174 and 175 now become (179)ad=Ad*e;g→Endg ; adξ=ddτ|τ=0Adexp(τξ)=ξg:η∈g↦...
Let M be a manifold with an action of a Lie group G, $\\A$ the functionalgebra on M. The first problem we consider is to construct a $U_h(\\g)$ invariantquantization, $\\A_h$, of $\\A$, where $U_h(\\g)$ is a quantum group correspondingt... J Donin - 《Mathematics》...
Letzter, Local finiteness of the adjoint action for quantized enveloping algebras, to appear.Anthony Joseph and Gail Letzter.Local finiteness of the adjoint action for quantized enveloping algebras. Journal of Algebra . 1992A. Joseph and G. Letzter, Local finiteness of the adjoint action for ...