3-Hom-Lie algebras based on \(\sigma\)-derivation and involution

DOI10.1007/S00006-020-01068-6zbMath1468.17031OpenAlexW3038125175MaRDI QIDQ2194016

Viktor Abramov, Sergei D. Silvestrov

Publication date: 25 August 2020

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

Full work available at URL: https://doi.org/10.1007/s00006-020-01068-6

zbMATH Keywords

Lie algebrasHom-Lie algebras3-Hom-Lie algebras

Mathematics Subject Classification ID

Ternary compositions (17A40) Hom-Lie and related algebras (17B61)

Related Items (13)

Representations and deformations of 3-Hom-ρ-Lie algebras ⋮ Classification, centroids and derivations of two-dimensional Hom-Leibniz algebras ⋮ Color hom-Lie algebras, color hom-Leibniz algebras and color omni-hom-Lie 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 ⋮ On Lie-type constructions over twisted derivations ⋮ On ideals and derived and central descending series of \(n\)-ary Hom-algebras ⋮ Tensor products and perturbations of BiHom-Novikov-Poisson algebras ⋮ Structure and cohomology of 3-Lie-Rinehart superalgebras

Cites Work

• Brackets with \((\tau,\sigma)\)-derivations and \((p,q)\)-deformations of Witt and Virasoro algebras
• The M2-M5 brane system and a generalized Nahm's equation
• \(n\)-Lie algebras
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• \(D\)-branes, monopoles and Nahm equations
• Quantum super Nambu bracket of cubic supermatrices and 3-Lie superalgebra
• 3-ary Hom-Lie superalgebras induced by Hom-Lie superalgebras
• Super 3-Lie algebras induced by super Lie algebras
• Deformations of Lie algebras using \(\sigma\)-derivations
• Quasi-hom-Lie algebras, central extensions and 2-cocycle-like identities
• Constructions of 3-Lie algebras
• Generalization of n-ary Nambu algebras and beyond
• Matrix 3-Lie superalgebras and BRST supersymmetry
• Generalized Hamiltonian Dynamics
• Ternary Hom–Nambu–Lie algebras induced by Hom–Lie algebras
• Structure and Cohomology of 3-Lie Algebras Induced by Lie Algebras

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