scholarly journals Combinatorial structures associated with low dimensional second class of non-Lie filiform Leibniz algebra

2017 ◽  
Author(s):  
A. A. S. Ahmad Jamri ◽  
Sh. K. Said Husain ◽  
I. S. Rakhimov
Keyword(s):  
Leibniz Algebra ◽  
Combinatorial Structures ◽  
Filiform Leibniz Algebra ◽  
Low Dimensional

scholarly journals Solvable Leibniz algebras whose nilradical is a quasi-filiform Leibniz algebra of maximum length

2019 ◽  
Vol 47 (4) ◽  
pp. 1578-1594
Author(s):  
Kobiljon K. Abdurasulov ◽  
Jobir Q. Adashev ◽  
José M. Casas ◽  
Bakhrom A. Omirov
Keyword(s):  
Maximum Length ◽  
Leibniz Algebra ◽  
Leibniz Algebras ◽  
Filiform Leibniz Algebra

scholarly journals Varieties of Null-Filiform Leibniz Algebras Under the Action of Hopf Algebras

2021 ◽  
Author(s):  
Lucio Centrone ◽  
Chia Zargeh
Keyword(s):  
Hopf Algebra ◽  
Free Algebra ◽  
Hopf Algebras ◽  
Leibniz Algebra ◽  
Module Structure ◽  
Leibniz Algebras ◽  
Finite Dimensional ◽  
Filiform Leibniz Algebra ◽  
Algebra Over A Field ◽  
Cocommutative Hopf Algebra

AbstractLet L be an n-dimensional null-filiform Leibniz algebra over a field K. We consider a finite dimensional cocommutative Hopf algebra or a Taft algebra H and we describe the H-actions on L. Moreover we provide the set of H-identities and the description of the Sn-module structure of the relatively free algebra of L.

scholarly journals Centroids and derivations of low-dimensional Leibniz algebra

2017 ◽  
Author(s):  
Sh. K. Said Husain ◽  
I. S. Rakhimov ◽  
W. Basri
Keyword(s):  
Leibniz Algebra ◽  
Low Dimensional

Finite-dimensional Leibniz algebras and combinatorial structures

2017 ◽  
Vol 20 (01) ◽  
pp. 1750004 ◽  
Author(s):  
M. Ceballos ◽  
J. Núñez ◽  
Á. F. Tenorio
Keyword(s):  
Leibniz Algebra ◽  
Combinatorial Structure ◽  
Combinatorial Structures ◽  
Leibniz Algebras ◽  
Finite Dimensional ◽  
Dimension 2

Given a finite-dimensional Leibniz algebra with certain basis, we show how to associate such algebra with a combinatorial structure of dimension 2. In some particular cases, this structure can be reduced to a digraph or a pseudodigraph. In this paper, we study some theoretical properties about this association and we determine the type of Leibniz algebra associated to each of them.

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