Hom-Jordan李代数的T~*-扩张
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摘要
通过Hom-Jordan李代数L的迷向Hom-理想J,得到L中存在包含J的极大迷向Hom-理想I,并得到L等距同构于L/I的某个T*-扩张或某个T*-扩张非退化的余维数为1的Hom-理想,进而给出Hom-Jordan李代数L的结构特征.
By using an isotropic Hom-ideal J of Hom-Jordan Lie algebra L,we obtained that L contained a maximally isotropic Hom-ideal Iof J,then L was isometric to a T*-extension of L/I or a nondegenerate Hom-ideal of codimension 1 in a T*-extension of L/I,moreover,we gave structure characteristics of Hom-Jordan Lie algebra L.
By using an isotropic Hom-ideal J of Hom-Jordan Lie algebra L,we obtained that L contained a maximally isotropic Hom-ideal Iof J,then L was isometric to a T*-extension of L/I or a nondegenerate Hom-ideal of codimension 1 in a T*-extension of L/I,moreover,we gave structure characteristics of Hom-Jordan Lie algebra L.
引文
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[9]马瑶,陈良云,林洁.李color代数的T*-扩张[J].数学年刊,2014,35A(5):623-638.(MA Yao,CHEN Liangyun,LIN Jie.T*-Extensions of Lie Color Algebras[J].Chinese Ann Math,2014,35A(5):623-638.)
[2]Kamiya N,Okubo S.A Construction of Simple Jordan Superalgebra of F Type from a Jordan-Lie Triple System[J].Ann Mat Pura Appl,2002,181(3):339-348.
[3]钱玲,周佳,陈良云.Jordan李代数的Engel定理及其应用[J].数学年刊,2012,33A(5):517-526.(QIAN Ling,ZHOU Jia,CHEN Liangyun.Engel’s Theorem of Jordan Lie Algebra and Its Applications[J].Chinese Ann Math,2012,33A(5):517-526.)
[4]Hartwig J T,Larsson D,Silvestrov S D.Deformations of Lie Algebras Usingσ-Derivations[J].J Algebra,2006,295(2):314-361.
[5]Benayadi S,Makhlouf A.Hom-Lie Algebras with Symmetric Invariant Nondegenerate Bilinear Forms[J].J Geom Phys,2014,76:38-60.
[6]LIU Yan,CHEN Liangyun,MA Yao.Representations and Module-Extensions of 3-Hom-Lie Algebras[J].J Geom Phys,2015,98:376-383.
[7]ZHAO Jun,CHEN Liangyun,MA Lili.Representations and T*-Extensions of Hom-Jordan-Lie Algebras[J].Comm Algebra,2016,44(7):2786-2812.
[8]Bordemann M.Nondegenerate Invariant Bilinear Forms on Nonassociative Algebras[J].Acta Math Univ Comenian,1997,66(2):151-201.
[9]马瑶,陈良云,林洁.李color代数的T*-扩张[J].数学年刊,2014,35A(5):623-638.(MA Yao,CHEN Liangyun,LIN Jie.T*-Extensions of Lie Color Algebras[J].Chinese Ann Math,2014,35A(5):623-638.)