Results 71 to 80 of about 277 (96)

Adjoint Functors and Representation Dimensions

Acta Mathematica Sinica, English Series, 2006
Let \(\widehat{\mathcal{C}}\) denote the category of coherent functors on a category \(\mathcal{C}\). Suppose that \(\mathcal{C}\) and \(\mathcal{D}\) are additive \(k\)-categories and that \(F,G\) is pair of adjoint functors between them. The author obtains comparisons of \(\text{ gl.dim}(\widehat{\mathcal{C}}) \) with \(\text{ gl.dim}(\widehat ...
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Exterior Powers of the Adjoint Representation

Canadian Journal of Mathematics, 1997
AbstractExterior powers of the adjoint representation of a complex semisimple Lie algebra are decomposed into irreducible representations, to varying degrees of satisfaction.
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Adjoint representations of exceptional Lie algebras

Theoretical and Mathematical Physics, 1987
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Ol'shanetskij, M. A., Rogov, V.-B. K.
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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
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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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