Results 251 to 260 of about 3,055 (272)

Cubic Forms on Adjoint Representations of Exceptional Groups

Journal of Mathematical Sciences, 2017
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Atamanova, M. M., Luzgarev, A. Yu.
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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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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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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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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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Self-Adjoint Representations of Commutative *-Algebras

1990
The results obtained in Section 8.4 have shown that a part of the representation theory of C*-algebras can be generalized to unbounded *-representations if, roughly speaking, the self-adjointness of certain *-representations is assumed. Thus seld-adjoint representations are basic objects in the theory of *-representations of general *-algebras. In this
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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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Adjoint Shape Optimisation Using Model Boundary Representation

2018
Manipulating CAD geometry using primitive components rather than the originating software is typically a challenging prospect. The parameterization used to define the geometry of a model is often integral to the efficiency of the design. However, it is not always possible to access these parameters due to the closed-source, non-standardized nature of ...
Marios Damigos, Eugene de Villiers
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Adjoint Representations of Symmetric Groups

2021
Mahir Bilen Can, Miles Jones
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