Generalized derivations and Rota-Baxter operators of \(n\)-ary Hom-Nambu superalgebras

DOI10.1007/s00006-020-01115-2OpenAlexW3152932079MaRDI QIDQ2029696

Othmen Ncib, Sami Mabrouk, Sergei D. Silvestrov

Publication date: 4 June 2021

Published in: Advances in Applied Clifford Algebras (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2003.01080

zbMATH Keywords

derivationsRota-Baxter operatorsquasiderivationsHom-Lie superalgebras\(n\)-ary Hom-Nambu superalgebras\(n\)-ary Nambu superalgebras\(n\)-Hom-Lie superalgebras3-Hom-pre-Lie algebras

Mathematics Subject Classification ID

Automorphisms, derivations, other operators (nonassociative rings and algebras) (17A36) Ternary compositions (17A40) Other (n)-ary compositions ((n ge 3)) (17A42) Hom-Lie and related algebras (17B61) Yang-Baxter equations and Rota-Baxter operators (17B38) (non-Lie) Hom algebras and topics (17D30)

Related Items (15)

Representations and deformations of 3-Hom-ρ-Lie algebras ⋮ Hom-Leibniz bialgebras and BiHom-Leibniz dendriform algebras ⋮ Classification, centroids and derivations of two-dimensional Hom-Leibniz algebras ⋮ Decomposition of complete color hom-Lie algebras ⋮ Hom-prealternative superalgebras ⋮ On classification of \((n+1)\)-dimensional \(n\)-Hom-Lie algebras with nilpotent twisting maps ⋮ On classification of (\(n +1\))-dimensional \(n\)-Hom-Lie algebras for \(n =4,5,6\) and nilpotent twisting map with 2-dimensional kernel ⋮ On \((\lambda,\mu,\gamma)\)-derivations of BiHom-Lie algebras ⋮ HNN-extension of involutive multiplicative Hom-Lie algebras ⋮ Simply complete Hom-Lie superalgebras and decomposition of complete Hom-Lie superalgebras ⋮ Kupershmidt operators on Hom-Malcev algebras and their deformation ⋮ On Lie-type constructions over twisted derivations ⋮ Admissible Hom-Novikov-Poisson and Hom-Gelfand-Dorfman color Hom-algebras ⋮ On ideals and derived and central descending series of \(n\)-ary Hom-algebras ⋮ Unnamed Item

Cites Work

• On \((n+1)\)-Hom-Lie algebras induced by \(n\)-Hom-Lie algebras
• Brackets with \((\tau,\sigma)\)-derivations and \((p,q)\)-deformations of Witt and Virasoro algebras
• A classification of low dimensional multiplicative Hom-Lie superalgebras
• Generalized derivations of Lie color algebras
• Hom-Lie algebras with symmetric invariant nondegenerate bilinear forms
• Hom-Lie superalgebras and Hom-Lie admissible superalgebras
• Leibniz and Lie algebra structures for Nambu algebra
• \((n+1)\)-ary derivations of simple \(n\)-ary algebras
• Representations of hom-Lie algebras
• Representations and cohomology of \(n\)-ary multiplicative Hom-Nambu-Lie algebras
• Graded quasi-Lie algebras of Witt type
• Centroid structures of \(n\)-Lie algebras
• On foundation of the generalized Nambu mechanics
• Generalized derivations of Lie algebras
• 3-ary Hom-Lie superalgebras induced by Hom-Lie superalgebras
• Generalized derivations of multiplicative \(n\)-ary \(\Hom\text{-}\Omega\) color algebras
• On hom-Lie superalgebras
• Generalized derivations of Hom-Lie triple systems
• \(\delta\)-derivations of prime Lie algebras
• On \(\delta\)-derivations of Lie algebras
• Ternary Lie superalgebras and Nambu-Hamilton equation in superspace
• Generalized derivations of \(n\)-BiHom-Lie algebras
• On \(n\)-ary generalization of BiHom-Lie algebras and BiHom-associative algebras
• Multiplicative \(n\)-Hom-Lie color algebras
• A review on Hom-Gerstenhaber algebras and Hom-Lie algebroids
• Some constructions of multiplicative \(n\)-ary Hom-Nambu algebras
• Rota-Baxter operators on pre-Lie superalgebras
• \((n+1)\)-ary derivations of semisimple Filippov algebras
• Super 3-Lie algebras induced by super Lie algebras
• Deformations of Lie algebras using \(\sigma\)-derivations
• On \(n\)-ary Hom-Nambu and Hom-Nambu-Lie algebras
• On classification of \(n\)-Lie algebras
• Quasi-Lie structure of \(\sigma \)-derivations of \(\mathbb C[t^{\pm 1}\)]
• Structure of low dimensional \(n\)-Lie algebras over a field of characteristic 2
• Quasi-hom-Lie algebras, central extensions and 2-cocycle-like identities
• \(L\)-modules, \(L\)-comodules and Hom-Lie quasi-bialgebras.
• Hom-algebra structures
• Enveloping algebras of Hom-Lie algebras
• Quasi-Lie deformations on the algebra \(\mathbb F[t/(t^N)\)]
• The Frattini subalgebra of \(n\)-Lie algebras
• Leibniz n-algebras
• Generalized derivations of (color)n-ary algebras
• Construction of n-Lie algebras and n-ary Hom-Nambu-Lie algebras
• Alternative algebras admitting derivations with invertible values and invertible derivations
• Classification of Low Dimensional 3-Lie Superalgebras
• Semi-commutative Galois Extension and Reduced Quantum Plane
• Generalized Derivations of Lie Superalgebras
• Constructing (n+ 1)-Lie algebras fromn-Lie algebras
• On Derivations of the Ternary Malcev Algebra M ₈
• Generalization of n-ary Nambu algebras and beyond
• On a graded q-differential algebra
• n-ary algebras: a review with applications
• Notes on 1-parameter formal deformations of Hom-associative and Hom-Lie algebras
• Graded q-Differential Algebra Approach to q-Connection
• On Generalized N-Complexes Coming from Twisted Derivations
• Hom-Lie Admissible Hom-Coalgebras and Hom-Hopf Algebras
• Lie Color and Hom-Lie Algebras of Witt Type and Their Central Extensions
• A Note on Quasi-Lie and Hom-Lie Structures of σ-Derivations of C=[Z 1 ±1 ,…,Z n ±1 ]
• Hom-algebras and homology
• The inner derivation algebras of (n+1) dimensional n Lie algebras⁺
• Generalized Hamiltonian Dynamics
• On $ \delta$-derivations of $ n$-ary algebras
• HOM-ALGEBRAS AND HOM-COALGEBRAS
• Algebraic Structures and Applications
• Rota–Baxter cosystems and coquasitriangular mixed bialgebras
• Ternary Hom–Nambu–Lie algebras induced by Hom–Lie algebras
• Realizations of 3-Lie algebras
• Structure and Cohomology of 3-Lie Algebras Induced by Lie Algebras
• Nilpotentn-Lie Algebras
• Quasi-Deformations of 𝔰𝔩₂(𝔽) Using Twisted Derivations
• Enveloping algebras of color hom-Lie algebras
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Generalized derivations and Rota-Baxter operators of \(n\)-ary Hom-Nambu superalgebras