On classification of \((n+1)\)-dimensional \(n\)-Hom-Lie algebras with nilpotent twisting maps

DOI10.1007/978-3-031-32009-5_19OpenAlexW4387014536MaRDI QIDQ6119348

Abdennour Kitouni, Sergei D. Silvestrov

Publication date: 22 March 2024

Published in: Non-commutative and Non-associative Algebra and Analysis Structures (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-031-32009-5_19

zbMATH Keywords

\(n\)-Hom-Lie algebraHom-algebra

Mathematics Subject Classification ID

Other (n)-ary compositions ((n ge 3)) (17A42) Hom-Lie and related algebras (17B61) (non-Lie) Hom algebras and topics (17D30)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On \((n+1)\)-Hom-Lie algebras induced by \(n\)-Hom-Lie algebras
• \(q\)-deformation of the Virasoro algebra with central extension
• Brackets with \((\tau,\sigma)\)-derivations and \((p,q)\)-deformations of Witt and Virasoro algebras
• Capable \(n\)-Lie algebras and the classification of nilpotent \(n\)-Lie algebras with \(s(A) = 3\)
• Hom-Lie algebras with symmetric invariant nondegenerate bilinear forms
• Classification of simple linearly compact \(n\)-Lie superalgebras
• Leibniz and Lie algebra structures for Nambu algebra
• Representations of hom-Lie algebras
• Representations and cohomology of \(n\)-ary multiplicative Hom-Nambu-Lie algebras
• Graded quasi-Lie algebras of Witt type
• On the multiplier of nilpotent \(n\)-Lie algebras
• Centroid structures of \(n\)-Lie algebras
• Theory of \(n\)-Lie algebras
• Applications of deformed oscillators
• Cyclic homology of differential operators, the Virasoro algebra and a \(q\)-analogue
• Characterizations of the quantum Witt algebra
• On foundation of the generalized Nambu mechanics
• 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
• On solvability and nilpotency for \(n\)-Hom-Lie algebras and \((n+1)\)-Hom-Lie algebras induced by \(n\)-Hom-Lie algebras
• Multiplicative \(n\)-Hom-Lie color algebras
• Some constructions of multiplicative \(n\)-ary Hom-Nambu algebras
• Generalized derivations and Rota-Baxter operators of \(n\)-ary Hom-Nambu superalgebras
• 3-Hom-Lie algebras based on \(\sigma\)-derivation and involution
• On classification of \((n+5)\)-dimensional nilpotent \(n\)-Lie algebras of class two
• 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
• 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
• Bialgebras, the classical Yang-Baxter equation and Manin triples for 3-Lie algebras
• GENERALIZED DEFORMED VIRASORO ALGEBRAS
• Leibniz n-algebras
• Construction of n-Lie algebras and n-ary Hom-Nambu-Lie algebras
• Classification of Low Dimensional 3-Lie Superalgebras
• Constructing (n+ 1)-Lie algebras fromn-Lie algebras
• Classification of (n + 2)-Dimensional Metric n-Lie Algebras
• Generalization of n-ary Nambu algebras and beyond
• n-ary algebras: a review with applications
• Notes on 1-parameter formal deformations of Hom-associative and Hom-Lie algebras
• On Generalized N-Complexes Coming from Twisted Derivations
• Lie Color and Hom-Lie Algebras of Witt Type and Their Central Extensions
• Hom-algebras and homology
• The inner derivation algebras of (n+1) dimensional n Lie algebras⁺
• Generalized Hamiltonian Dynamics
• Classifications of (n+k)-dimensional metricn-Lie algebras
• HOM-ALGEBRAS AND HOM-COALGEBRAS
• Algebraic Structures and Applications
• On classification of (n + 6)-dimensional nilpotent n-Lie algebras of class 2 with n ≥ 4
• Ternary Hom–Nambu–Lie algebras induced by Hom–Lie algebras
• Realizations of 3-Lie algebras
• Classification of (n+3)-dimensional metric n-Lie algebras
• Structure and Cohomology of 3-Lie Algebras Induced by Lie Algebras
• Quasi-Deformations of 𝔰𝔩₂(𝔽) Using Twisted Derivations
• A characterization of finite dimensional nilpotent Filippov algebras

This page was built for publication: On classification of \((n+1)\)-dimensional \(n\)-Hom-Lie algebras with nilpotent twisting maps