Low dimensional cohomology of Hom-Lie algebras and \(q\)-deformed \(W(2,2)\) algebra

DOI10.1007/S10114-013-2614-1zbMath1338.17005arXiv1208.5278OpenAlexW1979796532WikidataQ115385227 ScholiaQ115385227MaRDI QIDQ2453862

Hong You, Lamei Yuan

Publication date: 11 June 2014

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1208.5278

zbMATH Keywords

first cohomology groupderivationHom-Lie algebrassecond cohomology group\(q\)-deformed \(W(2,2)\) algebra

Mathematics Subject Classification ID

Structure theory for nonassociative algebras (17A60) Virasoro and related algebras (17B68) Nonassociative algebras satisfying other identities (17A30) Automorphisms, derivations, other operators (nonassociative rings and algebras) (17A36)

Cites Work

• Hom-Lie superalgebras and Hom-Lie admissible superalgebras
• Representations of hom-Lie algebras
• \(W\)-algebra \(W\)(2, 2) and the vertex operator algebra \({L(\frac{1}{2},\,0)\,\otimes\, L(\frac{1}{2},\,0)}\)
• Derivations and central extensions of finitely generated graded Lie algebras
• \(q\)-deformation of \(W(2, 2)\) Lie algebra associated with quantum groups
• Deformations of Lie algebras using \(\sigma\)-derivations
• Quasi-hom-Lie algebras, central extensions and 2-cocycle-like identities
• Hom-algebra structures
• Enveloping algebras of Hom-Lie algebras
• Hom-Lie Color Algebra Structures
• Notes on 1-parameter formal deformations of Hom-associative and Hom-Lie algebras
• Hom-algebras and homology

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