Results 31 to 40 of about 39,911 (195)
SciPost Physics, 2021 We propose a Leibniz algebra, to be called DD$^+$, which is a generalization of the Drinfel'd double. We find that there is a one-to-one correspondence between a DD$^+$ and a Jacobi--Lie bialgebra, extending the known correspondence between a Lie ...
Jose J. Fernandez-Melgarejo, Yuho Sakatani
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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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On Inner Derivations of Leibniz Algebras
MathematicsLeibniz algebras are generalizations of Lie algebras. Similar to Lie algebras, inner derivations play a crucial role in characterizing complete Leibniz algebras.
Sutida Patlertsin +2 more
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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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FRIEZE PATTERNS WITH COEFFICIENTS
Forum of Mathematics, Sigma, 2020 Frieze patterns, as introduced by Coxeter in the 1970s, are closely related to cluster algebras without coefficients. A suitable generalization of frieze patterns, linked to cluster algebras with coefficients, has only briefly appeared in an unpublished ...
MICHAEL CUNTZ +2 more
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A characterization of nilpotent Leibniz algebras
, 2012 W. A. Moens proved that a Lie algebra is nilpotent if and only if it admits an invertible Leibniz-derivation. In this paper we show that with the definition of Leibniz-derivation from W. A.
Fialowski, Alice +2 more
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Omni-Representations of Leibniz Algebras
Communications in Mathematical Research, 2023 In this paper, first we introduce the notion of an omni-representation of a Leibniz algebra $g$ on a vector space $V$ as a Leibniz algebra homomorphism from $g$ to the omni-Lie algebra $gl(V)⊕V.$ Then we introduce the omni-cohomology theory associated to omni-representations and establish the relation between omni-cohomology groups and Loday-Pirashvili
Liu, Zhangju, Sheng, Yunhe
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Methods of group theory in Leibniz algebras: some compelling results
Researches in Mathematics, 2021 The theory of Leibniz algebras has been developing quite intensively. Most of the results on the structural features of Leibniz algebras were obtained for finite-dimensional algebras and many of them over fields of characteristic zero.
I.Ya. Subbotin
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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 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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