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Register a new userOn anticommutative algebras for which $[R_a,R_b]$ is a derivation
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We study anticommutative algebras with the property that commutator of any two multiplications is a derivation.
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We describe all degenerations of three dimensional anticommutative algebras $mathfrak{Acom}_3$ and of three dimensional Leibniz algebras $mathfrak{Leib}_3$ over $mathbb{C}.$ In particular, we describe all irreducible components and rigid algebras in the corresponding varieties
Anticommutative Engel algebras of the first five degeneration levels are classified. All algebras appearing in this classification are nilpotent Malcev algebras.
The purpose of this paper is to introduce and investigate the notion of derivation for quandle algebras. More precisely, we describe the symmetries on structure constants providing a characterization for a linear map to be a derivation. We obtain a complete characterization of derivations in the case of quandle algebras of emph{dihedral quandles} over fields of characteristic zero, and provide the dimensionality of the Lie algebra of derivations. Many explicit examples and computations are given over both zero and positive characteristic. Furthermore, we investigate inner derivations, in the sense of Schafer for non-associative structures. We obtain necessary conditions for the Lie transformation algebra of quandle algebras of Alexander quandles, with explicit computations in low dimensions.
In this paper, we introduce the notion of a derivation of a Hom-Lie algebra and construct the corresponding strict Hom-Lie 2-algebra, which is called the derivation Hom-Lie 2-algebra. As applications, we study non-abelian extensions of Hom-Lie algebras. We show that iso- morphism classes of diagonal non-abelian extensions of a Hom-Lie algebra g by a Hom-Lie algebra h are in one-to-one correspondence with homotopy classes of morphisms from g to the derivation Hom-Lie 2-algebra DER(h).
The present article is a part of the study of solvable Leibniz algebras with a given nilradical. In this paper solvable Leibniz algebras, whose nilradicals is naturally graded quasi-filiform algebra and the complemented space to the nilradical has maximal dimension, are described up to isomorphism.
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