限制李超代数  

Restricted Lie Superalgebras

作　　者：孙丽萍[1] 刘文德[2] SUN Li-ping;LIU Wen-de(School of Applied Sciences,Harbin University of Science and Technology,Harbin 150080,China;School of Mathematical Sciences,Harbin Normal University,Harbin 150025,China)

机构地区：[1]哈尔滨理工大学应用科学学院,黑龙江哈尔滨150080 [2]哈尔滨师范大学数学科学学院,黑龙江哈尔滨150025

出　　处：《哈尔滨理工大学学报》2018年第4期145-147,152,共4页Journal of Harbin University of Science and Technology

基　　金：国家自然科学基金(11471090);黑龙江省自然科学基金(A2015017)

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.

关 键 词：限制 李超代数 包络 

分 类 号：O152.5[理学—数学]