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Cohomologies of Lie Algebras of Vector Fields with Coefficients in Adjoint Representations

open access: yesCohomologies of Lie Algebras of Vector Fields with Coefficients in Adjoint Representations
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Lie algebras with an algebraic adjoint representation revisited

Manuscripta Mathematica, 2012
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Antonio Fernández Lopez
exaly   +3 more sources

Euler’s difference table and the decomposition of tensor powers of the adjoint representation of the $$A_n$$ Lie algebra

Theoretical and Mathematical Physics(Russian Federation), 2022
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
A M Perelomov, Perelomov A M
exaly   +2 more sources

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.
Robert G Donnelly
exaly   +2 more sources

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.
exaly   +2 more sources

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