A Review on Hom-Gerstenhaber Algebras and Hom-Lie Algebroids

Mishra, Satyendra Kumar; Silvestrov, Sergei

doi:10.1007/978-3-030-41850-2_11

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Cited by 15 publications

(6 citation statements)

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“…Hom-Lie-Rinehart algebras and their extensions in the small dimension cohomology space was introduced and studied in [46]. Hom-Rinehart algebras have close relations with Hom-Gerstenhaber Algebras and Hom-Lie Algebroids [47,48].…”

Section: Introductionmentioning

confidence: 99%

Structure and cohomology of 3-Lie-Rinehart superalgebras

Hassine

Chtioui

Mabrouk

et al. 2021

Communications in Algebra

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Section: Introductionmentioning

confidence: 99%

Structure and cohomology of 3-Lie-Rinehart superalgebras

Hassine

Chtioui

Mabrouk

et al. 2021

Communications in Algebra

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“…Rota-Baxter bisystems and covariant bialgebras, Rota-Baxter cosystems, coquasitriangular mixed bialgebras, coassociative Yang-Baxter pairs, coassociative Yang-Baxter equation and generalizations of Rota-Baxter systems and algebras, curved O-operator systems and their connections with (tri)dendriform systems and pre-Lie algebras have been considered in [68][69][70]. Generalisations of derivations are important for Hom-Gerstenhaber algebras, Hom-Lie algebroids and Hom-Lie-Rinehart algebras and Hom-Poisson homology [75].…”

Section: Introductionmentioning

confidence: 99%

Generalized Derivations and Rota-Baxter Operators of $$\varvec{n}$$-ary Hom-Nambu Superalgebras

Mabrouk

Ncib

Silvestrov

2021

Adv. Appl. Clifford Algebras

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The aim of this paper is to generalise the construction of n-ary Hom-Lie bracket by means of an $$(n-2)$$ ( n - 2 ) -cochain of given Hom-Lie algebra to super case inducing n-Hom-Lie superalgebras. We study the notion of generalized derivations and Rota-Baxter operators of n-ary Hom-Nambu and n-Hom-Lie superalgebras and their relation with generalized derivations and Rota-Baxter operators of Hom-Lie superalgebras. We also introduce the notion of 3-Hom-pre-Lie superalgebras which is the generalization of 3-Hom-pre-Lie algebras.

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“…Hom-Lie-Rinehart algebras and their extensions in the small dimension cohomology space was introduced and studied in [45]. Hom-Rinehart algebras have close relations with Hom-Gerstenhaber Algebras and Hom-Lie Algebroids [46,47].…”

Section: Introductionmentioning

confidence: 99%