Results 21 to 30 of about 156 (136)
The Classical Hom–Leibniz Yang–Baxter Equation and Hom–Leibniz Bialgebras
Mathematics, 2022 In this paper, we first introduce the notion of Hom–Leibniz bialgebras, which is equivalent to matched pairs of Hom–Leibniz algebras and Manin triples of Hom–Leibniz algebras.
Shuangjian Guo +2 more
doaj +1 more source
On the nilpotent Leibniz–Poisson algebras
Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2012 In this article Leibniz and Leibniz–Poisson algebras in terms of correctness of different identities are investigated. We also examine varieties of these algebras. Let K be a base field of characteristics zero.
S. M. Ratseev, O. I. Cherevatenko
doaj +3 more sources
Applying Group Theory Philosophy to Leibniz Algebras: Some New Developments [PDF]
Advances in Group Theory and Applications, 2020 This survey is an attempt of describing of main contours of a recently developing general theory of Leibniz Algebras. This theory based on the employing of methods and approaches which are proved to be exceedingly effective in infinite group theory.
Leonid A. Kurdachenko +2 more
doaj +1 more source
On the influence of ideals and self-idealizing subalgebras on the structure of Leibniz algebras
Доповiдi Нацiональної академiї наук України, 2021 The subalgebra A of a Leibniz algebra L is self-idealizing in L, if A = IL (A) . In this paper we study the structure of Leibniz algebras, whose subalgebras are either ideals or self-idealizing.
L.A. Kurdachenko +2 more
doaj +1 more source
Maximal Solvable Leibniz Algebras with a Quasi-Filiform Nilradical
Mathematics, 2023 This article is part of a study on solvable Leibniz algebras with a given nilradical. In this paper, solvable Leibniz algebras, whose nilradical is naturally graded quasi-filiform algebra and the complemented space to the nilradical has maximal dimension,
Kobiljon Abdurasulov +2 more
doaj +1 more source
From Groups to Leibniz Algebras: Common Approaches, Parallel Results [PDF]
Advances in Group Theory and Applications, 2018 In this article, we study (locally) nilpotent and hyper-central Leibniz algebras. We obtained results similar to those in group theory. For instance, we proved a result analogous to the Hirsch-Plotkin Theorem for locally nilpotent groups.
L.A. Kurdachenko +2 more
doaj +1 more source
Қарағанды университетінің хабаршысы. Математика сериясы, 2023 In recent years there has been a great interest in the study of Zinbiel (dual Leibniz) algebras. Let A be Zinbiel algebra over an arbitrary field K and let e1,e2,...,em,... be a linear basis of A. In 2010 A.
D.M. Zhangazinova, A.S. Naurazbekova
doaj +1 more source
On Restricted Leibniz Algebras
Communications in Algebra, 2006 In this paper we prove that in prime characteristic there is a functor $-_{p-Leib}$ from the category of diassociative algebras to the category of restricted Leibniz algebras, generalizing the functor from associative algebras to restricted Lie algebras.
Dokas, Ioannis, Loday, Jean-Louis
openaire +3 more sources
Conjugacy of Cartan Subalgebras in Solvable Leibniz Algebras and Real Leibniz Algebras [PDF]
Algebras and Representation Theory, 2017 This paper is devoted to study the conjugacy of Cartan subalgebras in solvable Leibniz algebras. A Leibniz algebra is nonantisymmetric generalization of Lie algebras. Since proofs of conjugacy results in Lie algebras depend on antisymmetry property, the authors prove the analogues of conjugacy results by amending the arguments in Leibniz algebras.
Stitzinger, Ernie, White, Ashley
openaire +2 more sources
On a class of Leibniz algebras
International Journal of Advanced Mathematical Sciences, 2015 <p>We pointed out the class of Leibniz algebras such that the Killing form is non degenerate implies algebras are semisimple.</p>
Béré, Côme J. A. +2 more
openaire +3 more sources