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تسجيل مستخدم جديدOn exceptional nilpotents in semisimple Lie algebras
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We classify all pairs (m,e), where m is a positive integer and e is a nilpotent element of a semisimple Lie algebra, which arise in the classification of simple rational W-algebras.
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In this paper, first we introduce the notion of a twisted Rota-Baxter operator on a 3-Lie algebra $g$ with a representation on $V$. We show that a twisted Rota-Baxter operator induces a 3-Lie algebra structure on $V$, which represents on $g$. By this
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The symplectic structures on $3$-Lie algebras and metric symplectic $3$-Lie algebras are studied. For arbitrary $3$-Lie algebra $L$, infinite many metric symplectic $3$-Lie algebras are constructed. It is proved that a metric $3$-Lie algebra $(A, B)$
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