Modules Over Color Hom-Poisson Algebras

Bakayoko, Ibrahima

doi:10.4172/1736-4337.1000212

Cited by 20 publications

(15 citation statements)

References 13 publications

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“…Unless stated, in the sequel all the graded spaces are over the same abelian group G and the bicharacter will be the same for all the structures. For the rest of this section, we give basic facts about color Hom-algebras [5], [22], [27] and prove some results concerning color Hom-Poisson and color Hom-exible algebras.…”

Section: Preliminaries and Some Resultsmentioning

confidence: 99%

“…They are further studied in [26] where the author proved that the polarisation of a given Hom-algebra is a Hom-Poisson algebra if and only if this Hom-algebra is an admissible Hom-Poisson algebra. The purpose of this paper is to study color Hom-Poisson algebras which are rst introduced in [5]. For more informations on other color Hom-type algebras, the reader can refer to [1,3,5,20,27].…”

Section: Introductionmentioning

confidence: 99%

“…In Section 2, we recall basic notions concerning color Hom-algebras. Color Hom-Poisson algebras [5] are dened without the ε-commutativity condition. Here we give the denition of these color Hom-algebras by adding this condition (Denition 2.5) and then Hom-Poissons algebras could be seen as color Hom-Poisson algebras with G = {0}.…”

Section: Introductionmentioning

confidence: 99%

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Some characterizations of color Hom-Poisson algebras

Attan¹

2018

HJMS

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Section: Preliminaries and Some Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Some characterizations of color Hom-Poisson algebras

Attan¹

2018

HJMS

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“…Any Hom-associative color algebra carries a structure of a non-commutative Hom-Poisson color algebra with the ε-commutator bracket. More precisely : Lemma 2.13 [10] Let (A, µ, ε, α) be a Hom-associative color algebra. Then (A, µ, {·, ·} = µ−ε(·, ·)µ op , ε, α) is a non-commutative Hom-Poisson color algebra.…”

Section: Definition 24 a Hom-lie Color Algebra Is A Color Hommentioning

confidence: 99%

Constructing Hom-Poisson color algebras

Bakayoko¹,

Toure²

2019

ija

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We give some constructions of Hom-Poisson color algebras first from a Hom-associative color algebra which twisting map is an averaging operator, then from a given Hom-Poisson color algebra and an averaging operator and finally from a Hom-post-Poisson color algebra. Then we show that any Hom-pre-Poisson color algebra leads to a Hom-Poisson color algebra. Conversly, we prove that any Hom-Poisson color algebra turn to a Hom-pre-Poisson color algebra via Rota-Baxter operator.Koszul dualization. Some examples and related structures are given. Among other results, the authors proved in [5] that tridendriform and Rota-Baxter Lie algebras lead to the structures of post-Lie algebras. Post-Poisson algebras [6] are algebraic structures containing post-Lie algebras [4], [9] and pre-Poisson algebras [13] which contain pre-Lie algebras (or left-symmetric algebras) and Zinbiel algebras, both structures being connected by some compatibility conditions.Classical (or ordinary) algebras were extended to generalized (or color or graded) algebras, among which one can cite : Simple Jordan color algebras arising from associative graded algebras [11], Representations and cocycle twists of color Lie algebras [16], On the classification of 3-dimensional coloured Lie algebras [15]. These structures are well-known to physicists and to mathematicans studying differential geometry and homotopy theory. They were extended to the Hom-setting by studying Hom-Lie superalgebras, Rota-Baxter operator on pre-Lie superalgebras and beyound [8] and Hom-Lie color algebras [12]. Color Hom-Poisson algebras were introduced in [10] as generalization of Hom-Poisson algebras [1].The aim of this paper is to introduce and study the relationship among commutative Hom-tridendriform color algebras and Hom-post-Poisson color algebras. The paper is organized as follows. In section 2, we recall definition of Hom-Poisson color algebras and define averaging operator on Hom-associative and Hom-Lie color algebras. We introduce Hom-post-Lie color algebras, and give some procedures of construction of Hom-post-Lie color algebras form either a given one or from Hom-Lie Rota-Baxter color algebras. The section 3 is devoted to the main results of this paper i.e. some constructions of Hom-Poisson color algebras from other algebraic structures.Throughout this paper, all graded vector spaces are assumed to be over a field K of characteristic different from 2. PreliminariesWe give basic notions and give some of their properties.Let G be an abelian group. A vector space V is said to be a G-graded if, there exists a family (V a ) a∈G of vector subspaces of V such thatAn element x ∈ V is said to be homogeneous of degree a ∈ G if x ∈ V a . We denote H(V ) the set of all homogeneous elements in V .Let V = ⊕ a∈G V a and V = ⊕ a∈G V a be two G-graded vector spaces. A linear mapping f : V → V is said to be homogeneous of degree b if f (V a ) ⊆ V a+b , ∀a ∈ G.

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“…The maps ∆ and Γ will be called the structure maps of the Hom-Poisson comodule and the quadruple (M, ∆, Γ, β) will be called a Hom-Poisson comodule over (A, δ, γ, α). where we set δ(x) = x 1 ⊗ x 2 , γ(x) = x (1) ⊗ x (2) , ∆(m) = m (−1) ⊗ m (0) and Γ(m) = m [−1] ⊗ m [0] (without summation symbol, for symplicity).…”

Section: Hom-poisson Comodulesmentioning

confidence: 99%

Hom-alternative modules and Hom–Poisson comodules

Bakayoko¹,

Manga

2017

Afr. Mat.

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In this paper we introduce modules over both left and right Hom-alternative algebras. We give some constructions of left and right Hom-alternative modules and give various properties of both, as well as examples. Then, we prove that morphisms of left alternative algebras extend to morphisms of left Hom-alternative algebras. Next, we introduce comodules over Hom-Poisson coalgebras and show that we may obtain a structure map of a comodule over a Hom-Poisson coalgebra from a given one.

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Modules Over Color Hom-Poisson Algebras

Cited by 20 publications

References 13 publications

Some characterizations of color Hom-Poisson algebras

Some characterizations of color Hom-Poisson algebras

Constructing Hom-Poisson color algebras

Hom-alternative modules and Hom–Poisson comodules

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