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...
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....
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 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...
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,(...
(NB: This agreement between SO (3)'s adjoint representation and its natural physical interpretation is special to SO(3): it does not hold for other matrix Lie groups.) Finally, the infinitesimal generators of the adjoint action are given by differentiation. For example, using eq. 108, we ...
A unitary 'quantization commutes with reduction' map for the adjoint action of a compact Lie group Let K be a simply connected compact Lie group and T * ( K ) its cotangent bundle. We consider the problem of 'quantization commutes with reduction' for the adjoint action of K on T * (...
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...
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 lead to a sort of twice complex structure on the orbits. He focuses on the geometry of the flow defined by Nahm's equations which ...
We study one and two parameter quantizations of the function algebra on a semisimple orbit in the coadjoint representation of a simple Lie group subject to the condition that the multiplication on the quantized algebra is invariant under action of the Drinfeld-Jimbo quantum group. We prove that ...