Results 251 to 260 of about 139,367 (266)

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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The deduction of the Lax representation for constrained flows from the adjoint representation

Journal of Physics A: Mathematical and General, 1993
Summary: For \(x\)- and \(t_ n\)-finite-dimensional Hamiltonian systems obtained from the decompositions of zero-curvature equations, it is shown that their Lax representations can be deduced directly from the adjoint representations of the auxiliary linear problems.
Yishen Li, Yunbo Zeng
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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 Functors and Representation Dimensions

Acta Mathematica Sinica, English Series, 2006
We study the global dimensions of the coherent functors over two categories that are linked by a pair of adjoint functors. This idea is then exploited to compare the representation dimensions of two algebras. In particular, we show that if an Artin algebra is switched from the other, then they have the same representation dimension.
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The adjoint representation of fuzzy Lie algebras

Fuzzy Sets and Systems, 2001
The author extends the notion of the commutator of a Lie algebra by Zadeh's extension principle to a product of fuzzy subsets. A fuzzy subspace generated by the product of two fuzzy ideals is shown to be a fuzzy ideal. The product of fuzzy ideals is used to define the descending central series of a fuzzy ideal.
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On non self-adjoint representations of Lie algebras [PDF]

Integral Equations and Operator Theory, 1983
We consider a method for constructing all non self-adjoint representations of a Lie algebra with the help of its irreducible representations. The method is based on imbedding of a representation in a more complicated object called a colligation. As an application we consider the case of two dimensional non-abelian Lie algebra.
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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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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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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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