On the Universal $$\alpha $$ α -Central Extension of the Semi-direct Product of Hom-Leibniz Algebras

2015 ◽  
Vol 39 (4) ◽  
pp. 1579-1602
Author(s):  
J. M. Casas ◽  
N. Pacheco Rego
Keyword(s):  
Direct Product ◽  
Central Extension ◽  
Leibniz Algebras

Lie triple systems and Leibniz algebras

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Revaz Kurdiani
Keyword(s):  
Lie Algebra ◽  
Central Extension ◽  
Triple System ◽  
Leibniz Algebra ◽  
Universal Central Extension ◽  
Central Extensions ◽  
Lie Triple System ◽  
Triple Systems ◽  
Leibniz Algebras ◽  
Universal Central Extensions

AbstractThe present paper deals with the Lie triple systems via Leibniz algebras. A perfect Lie algebra as a perfect Leibniz algebra and as a perfect Lie triple system is considered and the appropriate universal central extensions are studied. Using properties of Leibniz algebras, it is shown that the Lie triple system universal central extension is either the universal central extension of the Leibniz algebra or the universal central extension of the Lie algebra.

Ganea Term for Homology of Leibniz n-Algebras

2005 ◽  
Vol 12 (04) ◽  
pp. 629-634 ◽  
Author(s):  
J. M. Casas
Keyword(s):  
Exact Sequence ◽  
Central Extension ◽  
Central Extensions ◽  
Leibniz Algebras

We extend the five-term exact sequence of homology with trivial coefficients of Leibniz n-algebras [Formula: see text] associated to a central extension of Leibniz n-algebras [Formula: see text] by means of a sixth term which is a generalization of the Ganea term for homology of Leibniz algebras. We use this sequence in order to analyze several questions related with the centre and central extensions of a Leibniz n-algebra.

On isomorphism criterion for a subclass of complex filiform Leibniz algebras

2017 ◽  
Vol 27 (07) ◽  
pp. 953-972
Author(s):  
I. S. Rakhimov ◽  
A. Kh. Khudoyberdiyev ◽  
B. A. Omirov ◽  
K. A. Mohd Atan
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Central Extension ◽  
Linear Deformation ◽  
Leibniz Algebras ◽  
Structure Constants ◽  
Filiform Lie Algebras ◽  
Filiform Lie Algebra ◽  
Isomorphism Criterion

In this paper, we present an algorithm to give the isomorphism criterion for a subclass of complex filiform Leibniz algebras arising from naturally graded filiform Lie algebras. This subclass appeared as a Leibniz central extension of a linear deformation of filiform Lie algebra. We give the table of multiplication choosing appropriate adapted basis, identify the elementary base changes and describe the behavior of structure constants under these base changes, then combining them the isomorphism criterion is given. The final result of calculations for one particular case also is provided.

scholarly journals On universal central extensions of Hom-Leibniz algebras

2014 ◽  
Vol 13 (08) ◽  
pp. 1450053 ◽  
Author(s):  
J. M. Casas ◽  
M. A. Insua ◽  
N. Pacheco Rego
Keyword(s):  
Lie Algebra ◽  
Central Extension ◽  
Chain Complex ◽  
Leibniz Algebra ◽  
Central Extensions ◽  
Leibniz Algebras ◽  
Leibniz Homology ◽  
Universal Central Extensions

In the category of Hom-Leibniz algebras we introduce the notion of Hom-co-representation as adequate coefficients to construct the chain complex from which we compute the Leibniz homology of Hom-Leibniz algebras. We study universal central extensions of Hom-Leibniz algebras and generalize some classical results, nevertheless it is necessary to introduce new notions of α-central extension, universal α-central extension and α-perfect Hom-Leibniz algebra due to the fact that the composition of two central extensions of Hom-Leibniz algebras is not central. We also provide the recognition criteria for these kind of universal central extensions. We prove that an α-perfect Hom-Lie algebra admits a universal α-central extension in the categories of Hom-Lie and Hom-Leibniz algebras and we obtain the relationships between both of them. In case α = Id we recover the corresponding results on universal central extensions of Leibniz algebras.

Equitable Total Coloring of Direct Product of Path and Cycle

2019 ◽  
Vol 10 (7) ◽  
pp. 1476-1481
Author(s):  
S. Moidheen Aliyar ◽  
S. Manimaran ◽  
K. Manikandan
Keyword(s):  
Direct Product ◽  
Total Coloring

On solvable Leibniz algebras whose nilradical has characteristic sequence (m1,m2,m3)

2018 ◽  
Vol 2018 (3) ◽  
pp. 4-17
Author(s):  
K.K. Abdurasulov ◽  
Drew Horton ◽  
U.X. Mamadaliyev
Keyword(s):  
Characteristic Sequence ◽  
Leibniz Algebras

Sport and nationalism in the Republic of North Macedonia

Focaal ◽  
2019 ◽  
pp. 1-13
Author(s):  
Vasiliki P. Neofotistos
Keyword(s):  
Direct Product ◽  
Nation Building ◽  
National History ◽  
Sports Teams ◽  
The Balkans ◽  
The North ◽  
Political Forces ◽  
The Republic

Using the Republic of North Macedonia as a case study, this article analyzes the processes through which national sports teams’ losing performance acquires a broad social and political significance. I explore claims to sporting victory as a direct product of political forces in countries located at the bottom of the global hierarchy that participate in a wider system of coercive rule, frequently referred to as empire. I also analyze how public celebrations of claimed sporting victories are intertwined with nation-building efforts, especially toward the global legitimization of a particular version of national history and heritage. The North Macedonia case provides a fruitful lens through which we can better understand unfolding sociopolitical developments, whereby imaginings of the global interlock with local interests and needs, in the Balkans and beyond.

On the g-hypergroupoids associated with g-hypergraphs

Filomat ◽  
2017 ◽  
Vol 31 (15) ◽  
pp. 4819-4831 ◽  
Author(s):  
Mehdi Farshi ◽  
Bijan Davvaz ◽  
Saeed Mirvakili
Keyword(s):  
Direct Product ◽  
Fundamental Relation ◽  
Join Space ◽  
Commutative Hypergroup ◽  
Regular Relation

In this paper, we associate a partial g-hypergroupoid with a given g-hypergraph and analyze the properties of this hyperstructure. We prove that a g-hypergroupoid may be a commutative hypergroup without being a join space. Next, we define diagonal direct product of g-hypergroupoids. Further, we construct a sequence of g-hypergroupoids and investigate some relationships between it?s terms. Also, we study the quotient of a g-hypergroupoid by defining a regular relation. Finally, we describe fundamental relation of an Hv-semigroup as a g-hypergroupoid.

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