In this paper, we consider Leibniz algebras with derivations. A pair consisting of a Leibniz algebra and a distinguished derivation is called a LeibDer pair. We define a cohomology theory for LeibDer pair with coefficients in a representation. We study central extensions of a LeibDer pair. In...
In this paper we study non-nilpotent non-Lie Leibniz F \mathbb{F} -algebras with one-dimensional derived subalgebra, where F \mathbb{F} is a field with char ( F ) ≠ 2 \operatorname{char}(\mathbb{F}) eq 2 . We prove that such an algebra is isomorphic to the direct sum of the...
Guo S., Zhang X., Wang S., On split regular Hom-Leibniz-Rinehart algebras. J. Math. Res. Appl., 2022, 42(5): 481–498 MathSciNet Google Scholar Hartwig J., Larsson D., Silvestrov S., Deformations of Lie algebras using σ-derivations. J. Algebra, 2006, 295(2): 314–361 Artic...
In this work n -dimensional filiform Leibniz algebras admitting a gradation of length ( n 1 ) are classified. Derivations of such algebras are also described.doi:10.1016/J.JALGEBRA.2007.12.014S. AlbeverioSh.A. AyupovB.A. OmirovA.Kh. Khudoyberdiyev...
Basing ourselves on the categorical notions of central extensions and commutators in the framework of semi-abelian categories relative to a Birkhoff subcategory, we study central extensions of Leibniz algebras with respect to the Birkhoff subcategory of Lie algebras, called \(\mathsf {Lie}\)-central...
In this paper, we present some basis properties concerning generalized derivations and their subalgebras of a Leibniz triple system and show that the quasi... X Wu,Y Ma,L Chen 被引量: 0发表: 2020年 Leibniz triple systems admitting a multiplicative basis Let T be an arbitrary Leibniz triple...
AbstractTensors.jl: Tensor algebra abstract type interoperability with vector bundle parameter Grassmann.jl: ⟨Leibniz-Grassmann-Clifford-Hestenes⟩ differential geometric algebra of multivector forms Leibniz.jl: Derivation operator algebras for tensor fields Reduce.jl: Symbolic parser generator for Julia...
The Grassmann package is designed to smoothly handle high-dimensional bivector algebras with headroom to spare. Although some of these calculations may have an initial delay, repeated calls are fast due to built-in caching and pre-compilation....
AncocheaBermúdezR.Campoamor-StursbergGordon and Breach Science PublishersLinear and Multilinear AlgebraAncochea Bermudez J., Campoamor-Stursberg R., An irreducible component of the variety of Leibniz algebras having trivial intersection with the variety of Lie algebras, Linear Multilinear Algebra, 62 (...
The n-dimensional p-filiform Leibniz algebras of maximum length have already been studied with 0 ≤ p ≤ 2. For Lie algebras whose nilindex is eq