Quasi-hom-Lie algebras, central extensions and 2-cocycle-like identities

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• 作者：Larsson ; Daniel ; Silvestrov ; Sergei D.
• 关键词：Deformations ; Central extensions ; Quasi-hom-Lie algebras ; (Color) Lie algebras ; Witt algebras ; Virasoro algebras ; Loop algebras
• 刊名：Journal of Algebra
• 出版年：2005
• 出版时间：June 15, 2005
• 年：2005
• 卷：288
• 期：2
• 页码：321-344
• 全文大小：207 K

文摘

This paper introduces the notion of a quasi-hom-Lie algebra, or simply, a qhl-algebra, which is a natural generalization of hom-Lie algebras introduced in a previous paper [J.T. Hartwig, D. Larsson, S.D. Silvestrov, Deformations of Lie algebras using σ-derivations, math.QA/0408064]. Quasi-hom-Lie algebras include also as special cases (color) Lie algebras and superalgebras, and can be seen as deformations of these by maps, twisting the Jacobi identity and skew-symmetry. The natural realm for these quasi-hom-Lie algebras is generalizations-deformations of the Witt algebra me=""mml1"">method=retrieve&_udi=B6WH2-4G35M6J-1&_mathId=mml1&_user=10&_cdi=6838&_rdoc=5&_handle=V-WA-A-W-WU-MsSAYWA-UUW-U-AAWCVWEYCY-AAWBUAUZCY-WCDBEWEZA-WU-U&_acct=C000050221&_version=1&_userid=10&md5=a2b1723403f41d53c9e38fc0563ee7c3"">mg src=""http://www.sciencedirect.com/cache/MiamiImageURL/B6WH2-4G35M6J-1-2/0?wchp=dGLbVzb-zSkzk"" alt=""Click to view the MathML source"" align=""absbottom"" border=""0"" height=11 width=10> of derivations on the Laurent polynomials me=""mml2"">method=retrieve&_udi=B6WH2-4G35M6J-1&_mathId=mml2&_user=10&_cdi=6838&_rdoc=5&_handle=V-WA-A-W-WU-MsSAYWA-UUW-U-AAWCVWEYCY-AAWBUAUZCY-WCDBEWEZA-WU-U&_acct=C000050221&_version=1&_userid=10&md5=85c1851858d066c1a8d1a54342c36d97"">mg src=""http://www.sciencedirect.com/cache/MiamiImageURL/B6WH2-4G35M6J-1-3/0?wchp=dGLbVzb-zSkzk"" alt=""Click to view the MathML source"" align=""absbottom"" border=""0"" height=17 width=58>. We also develop a theory of central extensions for qhl-algebras which can be used to deform and generalize the Virasoro algebra by centrally extending the deformed Witt type algebras constructed here. In addition, we give a number of other interesting examples of quasi-hom-Lie algebras, among them a deformation of the loop algebra.