Hom-Nijienhuis operators and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:msup><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mo>⁎</mml:mo></mml:mrow></mml:msup></mml:math>-extensions of hom-Lie superalgebras

Liu, Yan; Chen, Liangyun; Ma, Yao

doi:10.1016/j.laa.2013.06.006

Cited by 46 publications

(25 citation statements)

References 12 publications

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“…Definition 4.2. [15] Let (g, [·, ·], α) be a multiplicative Hom-Lie superalgebra and K be a field. The set of p-cochains on g with coefficients in K, which we denote by C p (g; K), is the set of skew-supersymmetric p-linear maps from g × · · · × g (p-times) to K:…”

Section: Solvability and Nilpotency Of 3-ary Multiplicative Hom-lie Smentioning

confidence: 99%

3-ary Hom-Lie Superalgebras Induced By Hom-Lie Superalgebras

Guan

Chen

Sun

2017

Adv. Appl. Clifford Algebras

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The purpose of this paper is to study the relationships between a Hom-Lie superalgebra and its induced 3-ary-Hom-Lie superalgebra. We provide an overview of the theory and explore the structure properties such as ideals, center, derived series, solvability, nilpotency, central extensions, and the cohomology.1 of how to construct ternary multiplications from the binary multiplication of a Hom-Lie algebra, a linear twisting map, and a trace function satisfying certain compatibility conditions; and it was shown that this method can be used to construct ternary Hom-Nambu-Lie algebras from Hom-Lie algebras. This construction was generalized to n-Lie algebras and n-Hom-Nambu-Lie algebras in [5].The reference [1] constructed super 3-Lie algebras(that is, 3-ary Lie superalgebras) by super Lie algebras(that is, Lie superalgebras). The reference [14] constructed (n + 1)-Hom-Lie algebras by n-Hom-Lie algebras. Inspired by the references [14] and [1], the paper generalizes them to the case of Hom-superalgebra. Its aim is to study the relationships between a Hom-Lie superalgebra and its induced 3-ary-Hom-Lie superalgebra. We explore the structure properties of objects such as ideals, center, derived series, solvability, nilpotency, central extensions, and the cohomology. In Section 2, we recall the basic notions for Hom-Lie superalgebras and the construction of 3-ary-Hom-Lie superalgebras induced by Hom-Lie superalgebras, we also give a new construction theorem for such algebras and give some basic properties. In Section 3, we define the notion of solvability and nilpotency for 3-ary-Hom-Lie superalgebras and discuss solvability and nilpotency of 3-ary-Hom-Lie superalgebras induced by Hom-Lie superalgebras. In Section 4, we recall the definition and main properties of central extensions of Hom-Lie superalgebras, and then we study central extensions of 3-ary-Hom-Lie superalgebras induced by Hom-Lie superalgebras. The Section 5 is dedicated to study the corresponding cohomology.

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Section: Solvability and Nilpotency Of 3-ary Multiplicative Hom-lie Smentioning

confidence: 99%

3-ary Hom-Lie Superalgebras Induced By Hom-Lie Superalgebras

Guan

Chen

Sun

2017

Adv. Appl. Clifford Algebras

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“…The notion of Hom-Lie algebras was introduced by Hartwig, Larsson and Silvestrov to describe the q-deformation of the Witt and the Virasoro algebras [1]. Since then, many authors have studied Hom-type algebras [2][3][4][5][6][7]. The notion of Lie color algebras was introduced as generalized Lie algebras in 1960 by Ree [8].…”

Section: Introductionmentioning

confidence: 99%

On split regular Hom-Lie color algebras

Cao

Chen

2017

Colloq. Math.

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We introduce the class of split regular Hom-Lie color algebras as the natural generalization of split Lie color algebras. By developing techniques of connections of roots for this kind of algebras, we show that such a split regular Hom-Lie color algebra L is of the form L = U + [j]∈Λ/∼ I [j] with U a subspace of the abelian graded subalgebra H and any I [j] , a well described ideal of L, satisfying [I [j] , I [k] ] = 0 if [j] = [k]. Under certain conditions, in the case of L being of maximal length, the simplicity of the algebra is characterized.

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“…In [7], α kderivations of Hom-Lie algebras were introduced and studied. In [6,9], we studied Hom-Nijienhuis operators and T *-extensions of Hom-Lie superalgebras and Hom-Jordan Lie algebras, extending the generalized derivation theory of Lie algebras given in [5]. Recently, similar researches were done for Lie conformal algebras in [4].…”

Section: Introductionmentioning

confidence: 99%

Deformations and generalized derivations of Hom-Lie conformal algebras

2017

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The purpose of this paper is to extend the cohomology and conformal derivation theories of the classical Lie conformal algebras to Hom-Lie conformal algebras. In this paper, we develop cohomology theory of Hom-Lie conformal algebras and discuss some applications to the study of deformations of regular Hom-Lie conformal algebras. Also, we introduce α k -derivations of multiplicative Hom-Lie conformal algebras and study their properties.

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Hom-Nijienhuis operators and T⁎-extensions of hom-Lie superalgebras

Cited by 46 publications

References 12 publications

3-ary Hom-Lie Superalgebras Induced By Hom-Lie Superalgebras

3-ary Hom-Lie Superalgebras Induced By Hom-Lie Superalgebras

On split regular Hom-Lie color algebras

Deformations and generalized derivations of Hom-Lie conformal algebras

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