Results 51 to 60 of about 670,256 (260)
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
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Versal Deformations of Leibniz Algebras [PDF]
Journal of K-Theory, 2008 AbstractIn this work we consider deformations of Leibniz algebras over a field of characteristic zero. The main problem in deformation theory is to describe all non-equivalent deformations of a given object. We give a method to solve this problem completely, namely work out a construction of a versal deformation for a given Leibniz algebra, which ...
Fialowski, Alice +2 more
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3-Leibniz bialgebras (3-Lie bialgebras)
, 2017 The aim of this paper is to extend the notion of bialgebra for Leibniz algebras (and Lie algebras) to $3$-Leibniz algebras (and $3$-Lie algebras) by use of the cohomology complex of $3$-Leibniz algebras.
Rezaei-Aghdam, A., Sedghi-Ghadim, L.
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Multipliers and unicentral Leibniz algebras [PDF]
Journal of Algebra and Its Applications, 2021 In this paper, we prove Leibniz analogues of results found in Peggy Batten’s 1993 dissertation. We first construct a Hochschild–Serre-type spectral sequence of low dimension, which is used to characterize the multiplier in terms of the second cohomology group with coefficients in the field.
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On the structure of low-dimensional Leibniz algebras: some revision
Algebra and discrete mathematics, 2022 Let L be an algebra over a field F with the binary operations + and [·,·]. Then L is called a left Leibniz algebra if [[a,b],c]=[a,[b,c]]−[b,[a,c]] for all a, b, c ∈ L. We describe the inner structure of left Leibniz algebras having dimension 3.
L. A. Kurdachenko, O. Pypka, I. Subbotin
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On Leibniz-Poisson special polynomial identities
Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2014 In this paper we study Leibniz-Poisson algebras satisfying polynomial identities. We study Leibniz-Poisson special and Leibniz-Poisson extended special polynomials.
Sergey M Ratseev, Olga I Cherevatenko
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The least dimonoid congruences on relatively free trioids
Математичні Студії, 2022 When Loday and Ronco studied ternary planar trees, they introduced types of algebras, called trioids and trialgebras. A trioid is a nonempty set equipped with three binary associative operations satisfying additional eight axioms relating these ...
A. V. Zhuchok
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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
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Communications in Algebra, 2016 A converse to Lie's theorem for Leibniz algebras is found and generalized. The result is used to find cases in which the generalized property, called triangulable, is 2-recognizeable; that is, if all 2-generated subalgebras are triangulable, then the algebra is also.
Burch, Tiffany, Stitzinger, Ernie
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On the structure of Leibniz algebras, whose subalgebras are ideals or core-free
Доповiдi Нацiональної академiї наук УкраїниAn algebra L over a field F is said to be a Leibniz algebra (more precisely, a left Leibniz algebra), if it satisfies the Leibniz identity: [[a, b], c] = [a, [b, c]] — [b, [a, c]] for all a, b, c ∈ L. Leibniz algebras are generalizations of Lie algebras.
V.A. Chupordia +2 more
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