Operads and triangulation of Loday’s diagram on Leibniz algebras
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DOI: 10.1007/s13370-016-0431-2
Abstract: We factor the classical functors $${ As}\mathop {\longrightarrow }\limits ^{-} { Lie}$$As⟶-Lie and $${ Dias}\mathop {\longrightarrow }\limits ^{-}{ Leib}$$Dias⟶-Leib through the categories $${ Pre}\hbox {-}{} { Lie}$$Pre-Lie and $${ Pre}\hbox {-}{} { Leib}$$Pre-Leib of two… read more here.
Keywords: loday diagram; leibniz algebras; operads triangulation; triangulation loday ... See more keywords
Local and 2-Local Derivations and Automorphisms on Simple Leibniz Algebras
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DOI: 10.1007/s40840-019-00799-5
Abstract: This paper is devoted to study local and 2-local derivations and automorphism of complex finite-dimensional simple Leibniz algebras. We show that all local derivations and 2-local derivations on a finite-dimensional complex simple Leibniz algebra are… read more here.
Keywords: leibniz; automorphisms simple; local derivations; local local ... See more keywords
Split 3-Leibniz algebras
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DOI: 10.1016/j.geomphys.2017.01.017
Abstract: Abstract We introduce and describe the class of split 3-Leibniz algebras as the natural extension of the class of split Lie algebras, split Leibniz algebras, split Lie triple systems and split 3-Lie algebras. More precisely,… read more here.
Keywords: split lie; leibniz algebras; geometry; algebras split ... See more keywords
Tensor hierarchies and Leibniz algebras
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DOI: 10.1016/j.geomphys.2019.05.014
Abstract: Tensor hierarchies are algebraic objects that emerge in gauging procedures in supergravity models, and that present a very deep and intricate relationship with Leibniz (or Loday) algebras. In this paper, we show that one can… read more here.
Keywords: hierarchies leibniz; tensor hierarchy; tensor hierarchies; leibniz algebras ... See more keywords
HNN-extensions of Leibniz algebras
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DOI: 10.1016/j.jalgebra.2019.05.014
Abstract: Abstract In this paper we construct HNN-extensions of diassociative algebras and Leibniz algebras and prove that every Leibniz algebra embeds into any of its HNN-extensions. We also prove that every Leibniz algebra with at most… read more here.
Keywords: extensions leibniz; leibniz algebra; hnn extensions; leibniz algebras ... See more keywords
Characterizing nilpotent Leibniz algebras by their multiplier
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DOI: 10.1016/j.jalgebra.2021.03.009
Abstract: Abstract In this paper, we characterize all finite dimensional nilpotent Leibniz algebras L for which ( dim ( L ) ) 2 − dim ( H L 2 ( L ) ) ≤… read more here.
Keywords: nilpotent leibniz; characterizing nilpotent; leibniz algebras; algebras multiplier ... See more keywords
Some notes on the second homology of Leibniz algebras
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DOI: 10.1080/00927872.2017.1335742
Abstract: ABSTRACT Some properties of the second homology and cover of Leibniz algebras are established. By constructing a stem cover, the second Leibniz homology and cover of abelian, Heisenberg Lie algebras and cyclic Leibniz algebras are… read more here.
Keywords: second homology; notes second; homology leibniz; leibniz algebras ... See more keywords
Criteria for solvability and supersolvability in Leibniz algebras
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DOI: 10.1080/00927872.2017.1372455
Abstract: ABSTRACT Leibniz algebras are certain generalization of Lie algebras. Recently, analyzing the structure of subalgebras, David Towers gave some criteria for the solvability and supersolvability of Lie algebras. In this paper we define analogues concepts… read more here.
Keywords: supersolvability leibniz; leibniz algebras; criteria solvability; solvability supersolvability ... See more keywords
On the dimension of the c-nilpotent Schur Lie-multiplier of Leibniz algebras
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DOI: 10.1080/00927872.2018.1499927
Abstract: Abstract The Schur -multiplier of Leibniz algebras is the Schur multiplier of Leibniz algebras defined relative to the Liezation functor. In this paper, we provide upperbounds for the dimensions of the c-nilpotent Schur -multiplier and… read more here.
Keywords: multiplier leibniz; leibniz algebras; lie; nilpotent schur ... See more keywords
Weak c-ideals of Leibniz algebras
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DOI: 10.1080/00927872.2023.2215340
Abstract: A subalgebra $B$ of a Leibniz algebra $L$ is called a weak c-ideal of $L$ if there is a subideal $C$ of $L$ such that $L=B+C$ and $B\cap C\subseteq B_{L}$ where $B_{L}$ is the largest… read more here.
Keywords: leibniz algebras; weak ideals; ideal; ideals leibniz ... See more keywords
Some Theorems on Leibniz n-Algebras from the Category Un (Lb)
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DOI: 10.1142/s1005386721000146
Abstract: We study the Leibniz n-algebra Un (L), whose multiplication is defined via the bracket of a Leibniz algebra L as [ x1, …, xn]= [x1, […,[ xn-2, [ x n-1, xn] ] … ] ].… read more here.
Keywords: theorems leibniz; leibniz algebras; algebras category;