Classification of a subclass of low-dimensional complex filiform Leibniz algebras

Rakhimov, I. S.; Husain, Sharifah Kartini Said

doi:10.1080/03081080903485702

Cited by 21 publications

(5 citation statements)

References 8 publications

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“…As for other classes in low dimensional cases they have been studied in [4], [6], [7] and [8]. The theoretical background of all these has been given by Rakhimov and Bekbaev in [5].…”

Section: Definition 2 An N-dimensional Leibniz Algebra L Is Said To Bmentioning

confidence: 98%

Isomorphism classes and invariants for a subclass of nine-dimensional filiform Leibniz algebras

Deraman

Rakhimov

Husain

2012

AIP Conference Proceedings

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“…As for other classes in low dimensional cases they have been studied in [4], [6], [7] and [8]. The theoretical background of all these has been given by Rakhimov and Bekbaev in [5].…”

Section: Definition 2 An N-dimensional Leibniz Algebra L Is Said To Bmentioning

confidence: 98%

Isomorphism classes and invariants for a subclass of nine-dimensional filiform Leibniz algebras

Deraman

Rakhimov

Husain

2012

AIP Conference Proceedings

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“…The classes of and have been classified up to dimension (see [3,5,6]). While the class of filiform Leibniz algebras appearing from the naturally graded filiform Lie algebras denoted by has been classified up to dimension (see [7]).…”

Section: Definition 1 An Algebra Over a Fieldmentioning

confidence: 99%

On isomorphism classes of a subclass of filiform leibniz algebras in dimension 10

Mohamed¹,

Husain²,

Rakhimov³

2014

AIP Conference Proceedings

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Some classes of filiform Leibniz algebras arising from the naturally graded non Lie filiform Leibniz algebras were introduced by Ayupov and Omirov in 2006. One of them is the first class of filiform Leibniz algebras and has been denoted by in fixed dimension Rakhimov and Bekbaev have suggested an approach of classifying based on algebraic invariants method. In terms of classification, it has been classified up to dimension 9 and the main purpose of this paper is to use method of invariants and apply to dimension 10. To complete this goal, we set up an isomorphism criterion, here we introduced some new functions to avoid big expressions involved in isomorphism criterion. From the criterion some lists of disjoint subsets from are obtained. These disjoint subsets are represented as a union of parametric family of orbits or just single orbits. For parametric cases, the invariants will be given.

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“…Since Loday's introduction of Leibniz algebras in 1993, many results of the theory of Lie algebras have been extended to Leibniz algebras. Nevertheless, a great deal of the results have been devoted to (co)homological problems [11,[16][17][18] or to the classification problems of nilpotent part and its subclasses [2,3,6,[20][21][22][23][24]. This is in contrast with the semisimple part of Leibniz algebras, which has been less studied.…”

Section: Introductionmentioning

confidence: 99%

On Leibniz Superalgebras with Even Part Corresponding to $\mathfrak {sl}_{2}$

Camacho

Navarro

2020

Algebr Represent Theor

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In this paper we describe finite-dimensional complex Leibniz superalgebras whose even part is the simple Leibniz algebra corresponding to sl 2 , i.e. its quotient algebra with respect to the Leibniz kernel I is isomorphic to sl 2 . We classify these Leibniz superalgebras in several cases with arbitrary dimensions in which the odd part is essentially a Leibniz irreducible (sl 2 I )-module or a finite direct sum of them.

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Classification of a subclass of low-dimensional complex filiform Leibniz algebras

Abstract: We give a complete classification of a subclass of complex filiform Leibniz algebras obtained from naturally graded non-Lie filiform Leibniz algebras. The isomorphism criteria in terms of invariant functions are given.

Cited by 21 publications

References 8 publications

Isomorphism classes and invariants for a subclass of nine-dimensional filiform Leibniz algebras

Isomorphism classes and invariants for a subclass of nine-dimensional filiform Leibniz algebras

On isomorphism classes of a subclass of filiform leibniz algebras in dimension 10

On Leibniz Superalgebras with Even Part Corresponding to $\mathfrak {sl}_{2}$

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