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 and abelian extensions of...
We deduce from our main theorem that this theory is exactly the Quillen cohomology for Leibniz n-algebras. 2. Derivations In the whole paper K is a ?eld. All tensor products are taken over K . Let A be a vector space equipped with an n-linear operation ω : A?n → A. A map f...
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...
Cited by (2) On N-graded vertex algebras associated with cyclic Leibniz algebras with small dimensions 2024, Journal of Pure and Applied Algebra Show abstract Local derivations of semisimple Leibniz algebras 2022, Communications in MathematicsView full text ...
Local and 2-Local Derivations of p-Filiform Leibniz Algebras Article 05 February 2020 The algebraic and geometric classification of nilpotent Leibniz algebras Article Open access 08 March 2025 3-filiform Leibniz algebras of maximum length Article 01 January 2016 Explore...
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...
fi on of Lie Algebras Using 0t—derivations[J ].J A1一 gebra,2005 ,295(2 ) :314 —361. [2 ] Makhlouf A ,Silvestrov S D.Hom—al gebra Structure [ J] .J.Gen.Lie Theory Appl,2008 ,2 (2 ) :51 —64 . [3 ] Cheng Yongsheng ,Su Yucai.( Co) Homology and ...
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....
Finally, we consider homotopy derivations onHLeib∞algebras and 2-derivations on Hom-Leibniz 2-algebras. The category of 2-termHLeib∞algebras with homotopy derivations is equivalent to the category of Hom-Leibniz 2-algebras with 2-derivations.Yizheng Li...
In this paper we show that the method for describing solvable Lie algebras with given nilradical by means of non-nilpotent outer derivations of the nilradical is also applicable to the case of Leibniz algebras. Using this method we extend the classification of solvable Lie algebras with naturally...