Results 191 to 200 of about 142,196 (212)

Adjoint Representations and the Derivative of exp

2020
In this chapter, in preparation for defining the Lie bracket on the Lie algebra of a Lie group, we introduce the adjoint representations of the group \(\mathbf {GL}(n, {\mathbb {R}})\) and of the Lie algebra \({\mathfrak {gl}}(n, {\mathbb {R}})\). The map \(\mathrm {Ad}\colon \mathbf {GL}(n, {\mathbb {R}})\rightarrow \mathbf {GL}({\mathfrak {gl}}(n ...
Jean Gallier, Jocelyn Quaintance
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The adjoint representation in rings of functions

Representation Theory of the American Mathematical Society, 1997
Let G G be a connected, simple Lie group of rank n n defined over the complex numbers. To a parabolic subgroup P P in G G of semisimple rank r r , one can associate n − r n-r positive integers coming from the theory of ...
Sommers, Eric, Trapa, Peter
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The Adjoint Representation and the Adjoint Action

2002
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 nilpotent orbits for short.
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LIE ALGEBRAS WITH AN ALGEBRAIC ADJOINT REPRESENTATION

Mathematics of the USSR-Sbornik, 1984
An algebra R over a field K satisfies the property P locally, if P holds for every finitely generated subalgebra of R. A famous result of A. I. Kostrikin claims that every Lie algebra G satisfying the Engel condition g(ad h)\({}^ n=0\) for any g,\(h\in G\), is locally nilpotent if char K\(=0\) or char K\(=p>n\).
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Cubic Forms on Adjoint Representations of Exceptional Groups

Journal of Mathematical Sciences, 2017
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Atamanova, M. M., Luzgarev, A. Yu.
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Adjoints, representables and limits

2014
We have approached the idea of universal property from three different angles, producing three different formalisms: adjointness, representability, and limits. In this final chapter, we work out the connections between them. In principle, anything that can be described in one of the three formalisms can also be described in the others.
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The Adjoint Representation of a Lie Group

1993
Every group G acts on itself by inner automorphisms: the map associated with an element g is h ↦ ghg −1. 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.
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Unitary Representations and Regularity for Self-adjoint Operators

1996
In this chapter we specialize some of the considerations of Chap. 5 to the case of unitary C 0-groups in a Hilbert space ℋ. The theory of unitary representations W(x) = e iA·x of ℝ n is a very well understood classical subject and will not be presented here.
Werner O. Amrein, Anne Boutet de Monvel, Vladimir Georgescu   +2 more
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The “Adjoint” Equation and Representation of Solutions

1971
In this section, we restrict our attention to the linear system $${\rm{\dot x}}\left( {\rm{t}} \right) = {\rm{L}}\left( {{\rm{t}},{\rm{x}}_{\rm{t}} } \right)$$ (17.1) where L(t,ϕ) is continuous in t,ϕ, linear in ϕ and is given explicitly by $${\rm{L}}\left( {{\rm{t}},{\rm{\phi }}} \right) = \sum\limits_{{\rm{k}} = 1}^\infty {{\rm{A}}_{\rm{
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The adjoint representation of left distributive structures

Communications in Algebra, 1992
We discuss some algebraic properties of the monoid generated by (left) translations in left distributive structures.This furnishes methods for enriching the original structure with a compatible associative product.
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