Results 131 to 140 of about 53,900 (153)

Invariants of the co-adjoint representation for Lie algebras of a special form

Russian Mathematical Surveys, 1996
An analytic function on the dual space of a Lie algebra is an invariant of the coadjoint representation provided that some conditions are fulfilled. This paper presents necessary and sufficient conditions.
Dmitrii Berzin
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A matrix Bernoulli equation in the adjoint matrix representation of simple three-dimensional Lie algebras [PDF]

Russian Mathematics, 2009
In this paper we give sufficient conditions for solvability by quadratures of a matrix Bernoulli equation whose parameters are defined in the adjointmatrix representation of simple threedimensional Lie algebras over a field of real numbers.
В. П. Деревенский
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On the first Cartan extensions of the adjoint representation of a simple Lie algebra [PDF]

Russian Mathematical Surveys, 1982
Ya S Krylyuk
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The algebra of polynomial invariants of the adjoint representation of the Lie superalgebra gl(m,n)

Communications in Algebra, 1997
Ivan Trishin, Issai Kantor
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The adjoint representation of a classical Lie algebra and the support of Kostant’s weight multiplicity formula

Journal of Combinatorics, 2016
Lauren Kelly Williams, Erik Insko, Pamela E. Harris   +2 more
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Adjoint representations of exceptional Lie algebras

Theoretical and Mathematical Physics, 1987
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
M. A. Ol'shanetskii, V. B. K. Rogov
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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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Extremal Bases for the Adjoint Representations of the Simple Lie Algebras

Communications in Algebra, 2006
We construct n distinct weight bases, which we call extremal bases, for the adjoint representation of each simple Lie algebra  of rank n: One construction for each simple root. We explicitly describe actions of the Chevalley generators on the basis elements. We show that these extremal bases are distinguished by their “supporting graphs” in three ways.
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Таблица эйлеровых разностей и разложение тензорных степеней присоединенного представления алгебры Ли $A_n$

Теоретическая и математическая физика, 2022
С использованием таблицы эйлеровых разностей получена простая явная формула для разложения $k$-й тензорной степени присоединенного представления алгебры Ли $A_n$ при $2k\le n+1$.
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On the adjoint representation of a free Lie algebra. II

[Part I, cf. Commun. Algebra 15, 2199-2207 (1987; Zbl 0633.17004).] Soit \(N\) le noyau de l'application \(\Gamma\) de l'idéal d'augmentation de l'algèbre enveloppante de \(L(X)\) sur \(L(X)\), l'algèbre de Lie libre sur \(X\), définie par \(\Gamma(x_ 1 \dots x_ n)= [x_ 1, [\dots [x_{n-1}, x_ n]\dots ]]\) pour \(x_ 1, \dots, x_ n\in X\).
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