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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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Invariants of the co-adjoint representation for Lie algebras of a special form
Russian Mathematical Surveys, 1996 Dmitrii Berzin
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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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Adjoint representations of exceptional Lie algebras
Theoretical and Mathematical Physics, 1987The recent development of superstring theory (1) has drawn attention to the potential importance of the exceptional Lie algebras (particularly E/sub 6/ and E/sub 8/) in a future unified theory. The paper consists of three parts. In the first, the authors consider normed algebras and the properties of their transformations.
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, 2006We 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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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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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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A SHORT PROOF OF ZELMANOV'S THEOREM ON LIE ALGEBRAS WITH AN ALGEBRAIC ADJOINT REPRESENTATION
, 2010 Antonio Fern
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