限制李超代数的环面秩  

Toral Ranks of Restricted Lie Superalgebras

作　　者：孙丽萍 刘文德 Li Ping SUN;Wen De LIU(College of Science,Harbin University of Science and Technology,Harbin 150080,P.R.China;School of Mathematics and Statistics,Hainan Normal University,Haikou 571158,P.R.China)

机构地区：[1]哈尔滨理工大学理学院,哈尔滨150080 [2]海南师范大学数学与统计学院,海口571158

出　　处：《数学学报（中文版）》2021年第1期167-176,共10页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助(11471090);黑龙江省自然科学基金资助(A2015017,QC2018006)。

摘　　要：本文将模李代数中环面与环面秩的理论推广到模李超代数中.应用模李超代数的限制包络得到了环面秩的若干重要性质.作为应用,计算了典型李超代数slm|n与限制Cartan型李超代数W(m,n,1),S(m,n,1)的绝对环面秩及S(m,n,1)在W(m,n,1)中的环面秩.In this paper,the definitions and properties of torus and toral rank are generalized from modular Lie algebras to super-case.Taking advantage of the restricted envelopes,we obtain certain important results concerning toral rank of modular Lie super algebras.As an application,the absolute toral ranks of the classical linear Lie superalgebra slm|n,the finite-dimensional restricted Lie superalgebras W(m,n,1) and S(m,n,1) of Cartan type and the toral rank of S(m,n,1) in W(m,n,1) are computed.

关 键 词：限制李超代数 限制包络 环面秩 

分 类 号：O152.5[理学—基础数学]