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Central polynomials for adjoint representations of simple Lie algebras exist
Summary: Yu. P. Razmyslov proved that for any finite dimensional reductive Lie algebra \({\mathfrak g}\) over a field \(K\) of zero characteristic (\(\dim_{K} \mathfrak G = m\)) and for its arbitrary associative enveloping algebra \(U\) with non-empty center \(Z(U)\) there exists a central polynomial which is multilinear and skew-symmetric in \(k ...Kagarmanov, A. A., Razmyslov, Yu. P.
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Invariants of adjoint and coadjoint representations of semidirect Lie algebras
Let \(\varphi\) be a (faithful) representation of a complex semisimple Lie algebra \(H\) in a linear space \(L\). Let \( A(\varphi)\) be the semidirect product of \(H\) by \(L\); its multiplication is defined as \([h+\ell, h_ 1+\ell_ 1]=[h,h_ 1]+\varphi(h)\ell_ 1-\varphi(h_ 1)\ell\).openaire +1 more source
Semi-invariants of a co-adjoint representation of Borel subalgebras of simple Lie algebras
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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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The Adjoint Representation for The Symmetry Lie Algebra of KdV Equation and its killing Type
, 2003 Jun Wang
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According to the classification of three-dimensional Lie algebras, there exist two simple Lie algebras \(L_ 3(\text{VIII})\) \((C^ 1_{12}= C^ 3_{23}= C^ 2_{13}/2= 1)\) and \(L_ 3(\text{IX})\) \((C^ 3_{12}= C^ 1_{23}= C^ 2_{31}= 1)\), where \(C^ i_{jk}\) are structure constants. Definition.
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The adjoint representation inside the exterior algebra of a simple Lie algebra
, 2013 Corrado De Concini +2 more
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