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...
Let G be a p-adic Lie group with Lie algebra and Ad: G鈫扐ut() be the adjoint representation. It was claimed in the literature that the kernel Kker(Ad) always has an abelian open normal subgroup. We show by means of a counterexample that this assertion is false. It can even happen...
Here we introduce this representation. But we lead up to it by first describing the adjoint representation of a Lie group on its own Lie algebra. Even apart from symplectic structure (and so applications in mechanics), both representations illustrate the ideas of previous Subsections. I will ...
伴随表示,adjoint representation 1)adjoint representation伴随表示 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...
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 ...
A Bia?Ynicki-Birula,JB Carrell,WM Mcgovern 摘要: 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 ...
According to Kirillov's idea, the irreducible unitary representations of a Lie group G roughly correspond to the coadjoint orbits O. In the forward direction one applies the methods of geometric quantization to produce a representation, ... 戴佳玲,Doug pickrell - CNKI 被引量: 4发表: 2004年 ...
(1997). The algebra of polynomial invariants of the adjoint representation of the Lie superalgebra gl( m , n ). Comm. Algebra. 25(7):2039–2070 MATH MathSciNetI.Kantor and I.Trishin, The algebra of polynomial invariants of the adjoint represen- tation of the Lie superalgebra gl(m|n)...
in a certain infinite-dimensional Hilbert space K. Now let C be a compact real form of B C , and denote by G the restriction of P C to C. As every strongly continuous unitary representation of a compact Lie group is completely reducible, we may decompose K ¼ ...
摘要: We formulate a second adjoint theorem in the context of tempered representations of real reductive groups, and prove it in the case of SL(2,R).关键词: Mathematics - Representation Theory Mathematics - Operator Algebras 22E45 DOI: 10.48550/arXiv.1603.08797 被引量: 5 ...