限制李超代数
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摘要
在单模李代数的分类中,限制李代数理论起到了重要作用。为了给单模李超代数的分类提供理论依据,丰富限制李超代数基本理论,研究了可限制李超代数及李超代数的限制包络和泛限制包络。证明了可限制李超代数是限制李超代数,给出了限制包络、泛限制包络的结构和性质。
The notion of restricted Lie algebras has played an important role in the modular Lie algebra theory,especially in the classification of the simple modular Lie algebras. It is necessary to develop restrictedness theory for the classification of the simple modular Lie superalgebras. In this paper,the restrictable Lie superalgebras,the restricted envelopes and universal restricted-envelope are studied. A restrictable Lie superalgebras is proved to be restricted Lie superalgebras. The structures and some properties of the restricted envelopes and universal p-envelope are obtained.
The notion of restricted Lie algebras has played an important role in the modular Lie algebra theory,especially in the classification of the simple modular Lie algebras. It is necessary to develop restrictedness theory for the classification of the simple modular Lie superalgebras. In this paper,the restrictable Lie superalgebras,the restricted envelopes and universal restricted-envelope are studied. A restrictable Lie superalgebras is proved to be restricted Lie superalgebras. The structures and some properties of the restricted envelopes and universal p-envelope are obtained.
引文
[1]STRADE H.Simple Lie Algebras over Fields of Characteristics I.Structure Theory[M].New York:Walter de Gruyter,2004.
[2]PREMET A,STRADE H.Classification of Finite Dimensional Simple Lie Algebras in Prime Characteristics[J].Contemporary Mathematics,2006,413:185-214.
[3]Ch EN L Y,MEND D J and Zhang Y Z.The Frattini Subalgebra of Restricted Lie Superalgebras[J].Acta Math.Sin.,English Ser.,2006,22(5):1343-1356.
[4]KOCHETKOV YU,LEITES D.Simple Lie algebras in Characteristic 2 Recovered from Superalgebras and on the Notion of a Simple Finite Group[J].Contemp.Math.,1992,131(2):59-67.
[5]PETROGRADSKI V M.Identities in the Enveloping Algebras for Modular Lie Superalgebras[J].J.Algebra,1992,145:1-21.
[6]SUN L P,LIU W D and GAO X C.Restrictered Envelopes of Lie Superalgebras[J].Algebra Colloquium,2015,22(2):309-320.
[7]LIU W D.Induced Modules of Restricted Lie Superalgebras[J].Northeastern Mathematical Journal,2005,21(1):54-60.
[8]SHU B,ZHANG C W.Representations of the Restricted Cartan Type Lie Superalgebra W(m,n,1)[J].Algebras and Representations Theory,2011,14(3):463-481.
[9]孙丽萍,刘文德,姚艳.Cartan型模李超代数H作为osp-模的分解与零维上同调[J].哈尔滨理工大学学报,2014,19(4):91-94.
[10]常远,刘文德.特征为3的奇Hamillton李超代数偶部的导子[J].哈尔滨理工大学报,2013,18(4):121-124.
[11]华秀英,刘文德.奇Hamiltonian李超代数偶部的非负Z-齐次导子空间[J].哈尔滨理工大学学报,2013,18(1):76-79.
[12]STRADE H,FARNSTEINER R.Modular Lie Algebras and Their Representations[M].New York:Monographys and Texbooks in Pure and Applied Mathematics,1988.
[2]PREMET A,STRADE H.Classification of Finite Dimensional Simple Lie Algebras in Prime Characteristics[J].Contemporary Mathematics,2006,413:185-214.
[3]Ch EN L Y,MEND D J and Zhang Y Z.The Frattini Subalgebra of Restricted Lie Superalgebras[J].Acta Math.Sin.,English Ser.,2006,22(5):1343-1356.
[4]KOCHETKOV YU,LEITES D.Simple Lie algebras in Characteristic 2 Recovered from Superalgebras and on the Notion of a Simple Finite Group[J].Contemp.Math.,1992,131(2):59-67.
[5]PETROGRADSKI V M.Identities in the Enveloping Algebras for Modular Lie Superalgebras[J].J.Algebra,1992,145:1-21.
[6]SUN L P,LIU W D and GAO X C.Restrictered Envelopes of Lie Superalgebras[J].Algebra Colloquium,2015,22(2):309-320.
[7]LIU W D.Induced Modules of Restricted Lie Superalgebras[J].Northeastern Mathematical Journal,2005,21(1):54-60.
[8]SHU B,ZHANG C W.Representations of the Restricted Cartan Type Lie Superalgebra W(m,n,1)[J].Algebras and Representations Theory,2011,14(3):463-481.
[9]孙丽萍,刘文德,姚艳.Cartan型模李超代数H作为osp-模的分解与零维上同调[J].哈尔滨理工大学学报,2014,19(4):91-94.
[10]常远,刘文德.特征为3的奇Hamillton李超代数偶部的导子[J].哈尔滨理工大学报,2013,18(4):121-124.
[11]华秀英,刘文德.奇Hamiltonian李超代数偶部的非负Z-齐次导子空间[J].哈尔滨理工大学学报,2013,18(1):76-79.
[12]STRADE H,FARNSTEINER R.Modular Lie Algebras and Their Representations[M].New York:Monographys and Texbooks in Pure and Applied Mathematics,1988.