Hom-Novikov color algebras

Bakayoko, Ibrahima

doi:10.48550/arxiv.1609.07813

Cited by 2 publications

(5 citation statements)

References 16 publications

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“…A Hom-ρ-algebra (A, •, ρ, φ) is said to be multiplicative if φ is a morphism for •, regular if φ is an automorphism for •, and involutive if φ 2 = Id A (see [2,3]).…”

Section: Hom-ρ-commutative Algebramentioning

confidence: 99%

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Riemannian geometry on Hom-$ρ$-commutative algebras

Bagheri¹,

Peyghan²

2018

Preprint

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Recently, some concepts such as Hom-algebras, Hom-Lie algebras, Hom-Lie admissible algebras, Hom-coalgebras are studied and some of classical properties of algebras and some geometric objects are extended on them. In this paper by recall the concept of Hom-ρ-commutative algebras, we intend to develop some of the most classical results in Riemannian geometry such as metric, connection, torsion tensor, curvature tensor on it and also we discuss about differential operators and get some results of differential calculus using them. The notions of symplectic structures and Poisson structures are included and an example of ρ-Poisson bracket is given.

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“…A Hom-ρ-algebra (A, •, ρ, φ) is said to be multiplicative if φ is a morphism for •, regular if φ is an automorphism for •, and involutive if φ 2 = Id A (see [2,3]).…”

Section: Hom-ρ-commutative Algebramentioning

confidence: 99%

“…Definition 2.5. [3] Let (A, ., ρ, φ) be a Hom-ρ-algebra. A ρ-derivation of degree |X| on A is a linear…”

Section: Hom-ρ-commutative Algebramentioning

confidence: 99%

Riemannian geometry on Hom-$ρ$-commutative algebras

Bagheri¹,

Peyghan²

2018

Preprint

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“…Example 3.9. Recall that a Hom-Novikov algebra [17], [20], is a triple (A, •, α) consisting of a vector space A, a bilinear map…”

Section: Hom-post-lie Modulesmentioning

confidence: 99%

“…In fact, we know that (A, [., . ], α) is a Hom-Lie algebra [35], [20]. The condition (3.2) comes from (3.6) and the left commutativity.…”

Section: Hom-post-lie Modulesmentioning

confidence: 99%

“…They have intensively investigated in the literature recently. Hom-type algebraic structures of many classical structures were studied as Hom-associative algebras, Hom-Lie admissible algebras and more general G-Hom-associative algebras [6], n-ary Hom-Nambu-Lie algebras [18], Rota-Baxter operators on pre-Lie superalgebras and beyond [1], Ternary Leibniz color algebras and beyond [24], Rota-Baxter Hom-Lie admissible algebras [3], Non-Commutative Ternary Nambu-Poisson Algebras and Ternary Hom-Nambu-Poisson Algebras [4], Laplacian of Hom-Lie quasi-bialgebras [23], Hom-Novikov color algebras [20], Hom-O-operators and Hom-Yang-Baxter equations [34], Some remarks on Hompath modules and Hom-path algebras [33]. And the refernces of these papers.…”

Section: Introductionmentioning

confidence: 99%

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Hom-post-Lie modules, O-operators and some functors on Hom-algebras

Bakayoko

2016

Preprint

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The aim of this paper is to study modules over Hom-post-Lie algebras and give some contructions and various twistings i.e. we show that modules over Hom-post-Lie algebras are close by twisting either by Hom-post-Lie algebra endomorphisms or module structure maps. Given a type of Hom-algebra A, an A-bimodule M and an O-operator T : A → M , we give construction of another Hom-algebra structure on M .Remark 2.2. If (A, [•, •]) is a non-necessarily associative algebra in the usual sense, we also regard it as the Hom-algebra (A, [•, •], Id A ) with identity twisting map.Definition 2.3. Let (A, [•, •], α) be a Hom-algebra. The Hom-associator of A is the trilinear map as α : A ⊗3 → A defined asDefinition 2.4. A Hom-associative algebra is a triple (A, •, α) consisting of a linear space A, a K-bilinear map • : A × A −→ A and a linear map α : A −→ A satisfying as α (x, y, z) = 0 (Hom-associativity), (2.1) for all x, y, z ∈ A.Definition 2.5. A Hom-module is a pair (M, α M ) in which M is a vector space and α M : M −→ M is a linear map.

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Hom-Novikov color algebras

Cited by 2 publications

References 16 publications

Riemannian geometry on Hom-$ρ$-commutative algebras

Riemannian geometry on Hom-$ρ$-commutative algebras

Hom-post-Lie modules, O-operators and some functors on Hom-algebras

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