Restricted hom-Lie algebras

Guan, Baoling; Chen, Liangyun

doi:10.15672/hjms.2015449439

Cited by 6 publications

(7 citation statements)

References 16 publications

(36 reference statements)

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“…The following theorem was obtained by Guan and Chen in [4] in the setting of Lie algebras. We extend it to Lie superalgebra case.…”

Section: Direct Sum Of Hom-lie Superalgebrasmentioning

confidence: 97%

“…The following theorem was proved by Baoling Guan and Liangyun Chen in [4] in the setting of Hom-Lie algebras.…”

Section: Preliminariesmentioning

confidence: 98%

“…Also, Hom-Lie color algebras, which are the natural generalizations of Hom-Lie algebras and Hom-Lie superalgebras, are studied by Yuan ([14]). However, the notion of restricted Hom-Lie algebras was introduced by Guan and Chen ( [4]). The Lie superalgebras were originally introduced by Kac ( [6]).…”

Section: Introductionmentioning

confidence: 99%

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Restricted Hom-Lie Superalgebras

Shaqaqha¹

2018

Preprint

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The aim of this paper is to introduce the notion of restricted Hom-Lie superalgebras. This class of algebras is a generalization of both restricted Hom-Lie algebras and restricted Lie superalgebras. In this paper, we present a way to obtain restricted Hom-Lie superalgebras from the classical restricted Lie superalgebras along with algebra endomorphisms. Homomorphisms relations between restricted Hom-Lie superalgebras are defined and studied. Also, we obtain some properties of p-maps and restrictable Hom-Lie superalgebras.

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“…The following theorem was obtained by Guan and Chen in [4] in the setting of Lie algebras. We extend it to Lie superalgebra case.…”

Section: Direct Sum Of Hom-lie Superalgebrasmentioning

confidence: 97%

“…The following theorem was proved by Baoling Guan and Liangyun Chen in [4] in the setting of Hom-Lie algebras.…”

Section: Preliminariesmentioning

confidence: 98%

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Restricted Hom-Lie Superalgebras

Shaqaqha¹

2018

Preprint

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“…Roughly speaking, one requires the existence of an endomorphism on the modular Lie algebra that resembles the pth power mapping x → x p in associative algebras. In the case of Hom-Lie algebra, there is a definition proposed in [24], but it turns out that this definition is not appropriate to queerify a restricted Hom-Lie algebras in characteristic 2, as done in [2] in the case of ordinary restricted Lie algebras. Here, we will give an alternative definition and justify the construction.…”

Section: P-structures and Queerification Of Hom-lie Algebras In Chara...mentioning

confidence: 99%

Hom-Lie Superalgebras in Characteristic 2

Bouarroudj,

Makhlouf

2023

Mathematics

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The main goal of this paper was to develop the structure theory of Hom-Lie superalgebras in characteristic 2. We discuss their representations, semidirect product, and αk-derivations and provide a classification in low dimension. We introduce another notion of restrictedness on Hom-Lie algebras in characteristic 2, different from the one given by Guan and Chen. This definition is inspired by the process of the queerification of restricted Lie algebras in characteristic 2. We also show that any restricted Hom-Lie algebra in characteristic 2 can be queerified to give rise to a Hom-Lie superalgebra. Moreover, we developed a cohomology theory of Hom-Lie superalgebras in characteristic 2, which provides a cohomology of ordinary Lie superalgebras. Furthermore, we established a deformation theory of Hom-Lie superalgebras in characteristic 2 based on this cohomology.

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“…At present, the discussion on the restricted Hom-structure has attracted more attention from scholars at home and abroad. In 2015, Guan [10] studied the structure of restricted Hom-Lie algebras. In [11], Shaqaqha introduced the restricted Hom-Lie Superalgebras.…”

Section: Introductionmentioning

confidence: 99%

Derivation Algebras of Restricted Hom-Lie Triple Systems

Zhou,

Dong,

et al. 2023

Fuzzy Systems and Data Mining IX

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In this paper, we investigate the properties of derivations of restricted Hom-Lie triple systems. By giving the concepts of derivations, generalized derivations, centroids and Hom-p-subsystems, we obtain some good results on generalized derivation algebras and their subalgebras, which including the subspace ℧ satisfying some conditions in the linear transformation End(L) is a restricted Hom-Lie triple system, the generalized derivation is a Hom-p-subsystem of ℧ and the central derivation is the intersection of the centroid and the derivation. The novelty of this paper is to discuss the derivation properties of Hom-Lie triple systems on the field 𝔽 of characteristic p, which makes the derivation structure of restricted Hom-Lie triple systems more complete.

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Restricted hom-Lie algebras

Cited by 6 publications

References 16 publications

Restricted Hom-Lie Superalgebras

Restricted Hom-Lie Superalgebras

Hom-Lie Superalgebras in Characteristic 2

Derivation Algebras of Restricted Hom-Lie Triple Systems

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