Results 1 to 10 of about 39,924 (177)
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
Representations of Leibniz Algebras [PDF]
Algebras and Representation Theory, 2014 This paper is devoted to the study of irreducible representations of Leibniz algebras. The authors establish a result which claims that irreducible Leibniz representations are very closely related to irreducible representations of the corresponding Lie algebra.
Fialowski, A., Mihálka, É. Zs.
openaire +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
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
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
Solvable Leibniz Algebras with Filiform Nilradical [PDF]
, 2015 In this paper we continue the description of solvable Leibniz algebras whose nilradical is a filiform algebra. In fact, solvable Leibniz algebras whose nilradical is a naturally graded filiform Leibniz algebra are described in [6] and [8].
Camacho Santana, Luisa María +2 more
core +1 more source
MINIMAL NONNILPOTENT LEIBNIZ ALGEBRAS
International Electronic Journal of Algebra, 2020 We classify all nonnilpotent, solvable Leibniz algebras with the property that all proper subalgebras are nilpotent. This generalizes the work of Stitzinger and Towers in Lie algebras. We show several examples which illustrate the differences between the Lie and Leibniz results.
BOSKO-DUNBAR, Lindsey +3 more
openaire +5 more sources
The local integration of Leibniz algebras [PDF]
, 2012 This article gives a local answer to the coquecigrue problem. Hereby we mean the problem, formulated by J-L. Loday in \cite{LodayEns}, is that of finding a generalization of the Lie's third theorem for Leibniz algebra.
Covez, Simon
core +2 more sources