On the structure of graded 3-Leibniz algebras

Khalili, Valiollah

doi:10.1080/00927872.2022.2162911

Cited by 2 publications

(3 citation statements)

References 28 publications

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“…Let us introduce the concepts of root-multiplicativity and maximal length in the framework of graded 3-Lie-Rinehart algebra, in a similar way to the ones for split Lie-Rinehart algebra in [22]. A) is a graded 3-Lie-Rinehart algebra such that L and A are ge-simple algebras then Z(L) = {0} = Ann(A) and Ann L (A) = {0}.…”

Section: Proposition 42 the Relationmentioning

confidence: 99%

“…For instance, in reference [6] the author studied the structure of arbitrary graded Lie algebras, being extended to the framework of graded Lie superalgebras in [9] by the technique of connections of elements in the support of the graing. Recently, in [7,8,22], the structure of arbitrary graded commutative algebras, graded Lie triple systems and graded 3-Leibniz algebras have been determined by the connections of the support of the grading.…”

Section: Introductionmentioning

confidence: 99%

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On the structure of graded $3$-Lie-Rinehart algebras

Khalili¹

2023

Preprint

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We study the structure of a graded 3-Lie-Rinehart algebra L over an associative and commutative graded algebra A. For G an abelian group, we show that if (L, A) is a tight G-graded 3-Lie-Rinehart algebra, then L and A decompose as L = i∈I L i and A = j∈J A j , where any L i is a non-zero graded ideal of L satisfying [L i1 , L i2 , L i3 ] = 0 for any i 1 , i 2 , i 3 ∈ I different from each other, and any A j is a non-zero graded ideal of A satisfying A j A l = 0 for any l, j ∈ J such that j = l, and both decompositions satisfy that for any i ∈ I there exists a unique j ∈ J such that A j L i = 0. Furthermore, any (L i , A j ) is a graded 3-Lie-Rinehart algebra. Also, under certain conditions, it is shown that the above decompositions of L and A are by means of the family of their, respectively, graded simple ideals.

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Section: Proposition 42 the Relationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On the structure of graded $3$-Lie-Rinehart algebras

Khalili¹

2023

Preprint

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“…Since then, the interest on gradings by the technique of connections of elements in the support of the graing on different classes of algebras has been remarkable in the recent years, motivated in part by their application in physics and geometry. Recently, in [7,12,13,16,17,18,28], the structure of graded Lie algebras, graded Lie superalgebras, graded Leibniz algebras, graded Lie triple systems, graded Leibniz triple systems, graded Lie algebra of order 3 and graded 3-Leibniz algebras have been determined by the connections of the support of the grading.…”

Section: Introductionmentioning

confidence: 99%

The structure of split regular Hom-Leibniz–Poisson color algebras

Khalili

2021

Asian-European J. Math.

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In this paper, we introduce the class of split regular Hom-Leibniz–Poisson color algebras as the natural generalization of split regular Hom-Leibniz algebras, split regular Hom-Poisson algebras and split regular Hom-Leibniz–Poisson superalgebras. By developing techniques of connections of roots for this kind of algebras, we show that such a split regular Hom-Leibniz–Poisson color algebra [Formula: see text] is of the form [Formula: see text], with [Formula: see text] a subspace of the abelian sub algebra [Formula: see text] and any [Formula: see text] a well-described ideal of [Formula: see text], satisfying [Formula: see text] if [Formula: see text] Under certain conditions, in the case of [Formula: see text] being of maximal length, the simplicity and the primeness of the algebra is characterized and it is shown that [Formula: see text] is the direct sum of the family of its minimal ideals, each one being a simple split regular Hom-Leibniz–Poisson color algebra.

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On the structure of graded 3-Leibniz algebras

Cited by 2 publications

References 28 publications

On the structure of graded $3$-Lie-Rinehart algebras

On the structure of graded $3$-Lie-Rinehart algebras

The structure of split regular Hom-Leibniz–Poisson color algebras

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