广义S-型模李超代数的结构
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摘要
通过确定元素形式较简单多项式代数的理想,得到了除幂代数、外代数和多项式代数作张量积的结合超代数理想以及广义模李超代数■的理想,进而给出广义模李超代数■的非单性及■限制李超代数的充要条件.
By determining the ideal of the polynomial algebra of simple element form,we obtained the combined superalgebraic ideal of the tensor product of the divided power algebra,the external algebra and the polynomial algebra,and the ideal of the generalized modular Lie superalgebra ■.Then we gave the nonsimplicity of generalized modular Lie superalgebra ■ and the necessary and sufficient conditions that ■ was a restricted Lie superalgebra.
By determining the ideal of the polynomial algebra of simple element form,we obtained the combined superalgebraic ideal of the tensor product of the divided power algebra,the external algebra and the polynomial algebra,and the ideal of the generalized modular Lie superalgebra ■.Then we gave the nonsimplicity of generalized modular Lie superalgebra ■ and the necessary and sufficient conditions that ■ was a restricted Lie superalgebra.
引文
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[6]周佳,赵昕,张宇.Hom-Leibniz代数的广义导子[J].吉林大学学报(理学版),2017,55(2):195-200.(ZHOU Jia,ZHAO Xin,ZHANG Yu.Generalized Derivations of Hom-Leibniz Algebras[J].Journal of Jilin University(Science Edition),2017,55(2):195-200.)
[7]ZHANG Qingcheng,ZHANG Yongzheng.Derivation Algebras of the Modular Lie Superalgebras W and S of Cartan-Type[J].Acta Math Sci,2000,20(1):137-144.
[8]LIU Wende,YUAN Jixia.Special Odd Lie Superalgebras in Prime Characteristic[J].Sci China Math,2012,55(3):567-576.
[2]KAC V G.Lie Superalgebras[J].Adv Math,1977,26(1):8-96.
[3]ZHAO Jun,CHEN Liangyun,MA Lili.Representations and T*-Extensions of Hom-Jordan-Lie Algebras[J].Comm Algebra,2016,44(7):2786-2812.
[4]CHEN Liangyun,MA Yao,NI Lin.Generalized Derivations of Lie Color Algebras[J].Results Math,2013,63(3/4):923-936.
[5]周佳,牛艳君,陈良云.Hom-李代数的广义导子[J].数学学报(中文版),2015,58(4):551-558.(ZHOU Jia,NIU Yanjun,CHEN Liangyun.Generalized Derivations of Hom-Lie Algebras[J].Acta Mathematica Sinica(Chinese Series),2015,58(4):551-558.)
[6]周佳,赵昕,张宇.Hom-Leibniz代数的广义导子[J].吉林大学学报(理学版),2017,55(2):195-200.(ZHOU Jia,ZHAO Xin,ZHANG Yu.Generalized Derivations of Hom-Leibniz Algebras[J].Journal of Jilin University(Science Edition),2017,55(2):195-200.)
[7]ZHANG Qingcheng,ZHANG Yongzheng.Derivation Algebras of the Modular Lie Superalgebras W and S of Cartan-Type[J].Acta Math Sci,2000,20(1):137-144.
[8]LIU Wende,YUAN Jixia.Special Odd Lie Superalgebras in Prime Characteristic[J].Sci China Math,2012,55(3):567-576.