BiHom-alternative, BiHom-Malcev and BiHom-Jordan algebras

The aim of this paper is to deal with BiHom-alternative algebras which are a generalization of alternative and Hom-alternative algebras, their structure is defined with two commuting multiplicative linear maps. We study cohomology and one-parameter formal deformation theory of left BiHom-alternative algebras. Moreover, we study central and $T_\theta$-extensions of BiHom-alternative algebras and their relationship with cohomology. Finally, we investigate generalized derivations and give some relevant results.

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“…In this section, we give some basics and properties on left BiHom-alternative algebras. We refer for the definitions to [7].…”

Section: Preliminaries and Basicsmentioning

confidence: 99%

“…In [22], BiHom-pre-Lie algebras and BiHom-Leibniz algebras were defined and studied via Rota-Baxter operators. The BiHom-versions of alternative, pre-alternative, quadri-alternative and Malcev algebras were introduced in [7] and [8]. The authors gave several constructions connecting such structures.…”

Section: Introductionmentioning

confidence: 99%

Deformations and Extensions of BiHom-alternative algebras

Chtioui

Mabrouk

Makhlouf

2023

International Electronic Journal of Algebra

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“…Hom-M-dendriform algebra gives rise to a Hom-pre-Malcev algebra and a Hom-Malcev algebra, in the same way as Hom-L-dendriform algebra, gives rise to Hom-pre-Lie algebra and Hom-Lie algebra (see [14,15,35] for more details).…”

Section: [[X Y] α(Z)]+[[y Z] α(X)]+[[z X] α(Y)]mentioning

confidence: 99%

Dendrification of Hom-Malcev algebras

Harrathi¹,

Mabrouk²,

Ncib³

et al. 2022

Preprint

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The main goal of this work is to introduce the notion of Hom-M-dendriform algebras which are the dendriform version of Hom-Malcev algebras. In fact they are the algebraic structures behind the O-operator of Hom-pre-Malcev algebras. They also fit into a bigger framework as Hom-Malcev algebraic analogues of Hom-L-dendriform algebras. Furthermore, we show a connections between Hom-M-Dendriform algebras and Hom-alternative quadri-algebras.

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“…The anti-commutator of a Hom-pre-Malcev algebra is a Hom-Malcev algebra and the left multiplication operators give a representation of this Hom-Malcev algebra, which is the beauty of such a structure. Similarly, a Hom-M-dendriform algebra gives rise to a Hom-pre-Malcev algebra, and a Hom-Malcev algebra, in the same way as Hom-L-dendriform algebra, gives rise to Hom-pre-Lie algebra and Hom-Lie algebra (see [13,14,43] for more details).…”

Section: Introductionmentioning

confidence: 99%

Hom-pre-Malcev and Hom-M-Dendriform algebras

Harrathi¹,

Mabrouk²,

Ncib³

et al. 2021

Preprint

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The purpose of this paper is to introduce and study the notion of Hom-pre-Malcev algebra which may be seen as a Malcev algebra whose product can be decomposed into two compatible pieces. We show also that bimodules over Malcev and pre-Malcev are twisted into bimodules over Hom-Malcev and Hom-pre-Malcev via endomorphisms respectively. Furthermore, we introduce the notion of Hom-M-dendriform algebra and show the connections between all these algebraic structures using O-operators.

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BiHom-alternative, BiHom-Malcev and BiHom-Jordan algebras

Cited by 15 publications

References 19 publications

Deformations and Extensions of BiHom-alternative algebras

Deformations and Extensions of BiHom-alternative algebras

Dendrification of Hom-Malcev algebras

Hom-pre-Malcev and Hom-M-Dendriform algebras

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