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We observe several facts and make conjectures about commutative algebras satisfying the Jacobi identity. The central question is which of those algebras admit a faithful representation (i.e., in Lie parlance, satisfy the Ado theorem, or, in Jordan parlance, are special).
For a simple Lie algebra, over $mathbb{C}$, we consider the weight which is the sum of all simple roots and denote it $tilde{alpha}$. We formally use Kostants weight multiplicity formula to compute the dimension of the zero-weight space. In type $A_r
All gradings by abelian groups are classified on the following algebras over an algebraically closed field of characteristic not 2: the simple Lie algebra of type $G_2$ (characteristic not 3), the exceptional simple Jordan algebra, and the simple Lie algebra of type $F_4$.
In this paper we initiate the study of the maximal subalgebras of exceptional simple classical Lie algebras g over algebraically closed fields k of positive characteristic p, such that the prime characteristic is good for g. In this paper we deal wit
After recalling the notion of Lie algebroid, we construct these structures associated with contact forms or systems. We are then interested in particular classes of Lie Rinehart algebras.
In this paper, we introduce the notion Lie-derivation. This concept generalizes derivations for non-Lie Leibniz algebras. We study these Lie-derivations in the case where their image is contained in the Lie-center, call them Lie-central derivations.