scholarly journals Residually solvable extensions of an infinite dimensional filiform Leibniz algebra

2021 ◽  
Author(s):  
K.K. Abdurasulov ◽  
B.A. Omirov ◽  
I.S. Rakhimov ◽  
G.O. Solijanova
Keyword(s):  
Leibniz Algebra ◽  
Infinite Dimensional ◽  
Filiform Leibniz Algebra

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 Leibniz algebras: a brief review of current results

2019 ◽  
Vol 11 (2) ◽  
pp. 250-257
Author(s):  
V.A. Chupordia ◽  
A.A. Pypka ◽  
N.N. Semko ◽  
V.S. Yashchuk
Keyword(s):  
Leibniz Algebra ◽  
Infinite Dimensional ◽  
Binary Operations ◽  
Leibniz Algebras ◽  
Finite Dimensional ◽  
Algebra Over A Field

Let $L$ be an algebra over a field $F$ with the binary operations $+$ and $[\cdot,\cdot]$. Then $L$ is called a left Leibniz algebra if it satisfies the left Leibniz identity $[[a,b],c]=[a,[b,c]]-[b,[a, c]]$ for all $a,b,c\in L$. This paper is a brief review of some current results, which related to finite-dimensional and infinite-dimensional Leibniz algebras.

Some infinite dimensional Leibniz bimodules of sl2

2021 ◽  
Vol 65 (3) ◽  
pp. 113-125
Keyword(s):  
Lie Algebra ◽  
Leibniz Algebra ◽  
Verma Modules ◽  
Infinite Dimensional ◽  
Direct Sum

In this paper, we study the infinite-dimensional bimodule of Leibniz algebra over sl2, which, as a module of the Lie algebra, splits into the direct sum of two simple sl2-modules, the so-called Verma modules. We prove that in this case there is exist only two indecomposable sl2-bimodule of Leibniz.

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