A family of transitive modular Lie superalgebras with depth one

作     者：Wen-de LIU~(1+) Yong-zheng ZHANG~2 ~1 Department of Mathematics,Harbin Normal University,Harbin 150080,China ~2 Department of Mathematics,Northeast Normal University,Changchun 130024,China 

作者机构：Department of Mathematics Harbin Normal University Harbin China Department of Mathematics Northeast Normal University Changchun China 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2007年第50卷第10期

页      面：1451-1466页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：This work is partially supported by the National Natural Science Foundation of China(Grant No.10671160) China Postdoctoral Science Foundation(Grant No.20060400107) 

主　　题：flag, divided power algebra, modular Lie superalgebra, embedding theorem 

摘      要：The embedding theorem is established for Z-graded transitive modular Lie superalgebras g■■■(g-1)satisfying the conditions: (i)g0■■(g-1) and g0-module g-1 is isomorphic to the natural■(g-1)-module; (ii)dim g1=2/3n(2n^2+1),where n=1/2dim g-1. In particular,it is proved that the finite-dimensional simple modular Lie superalgebras satisfying the conditions above are isomorphic to the odd Hamiltonian *** restricted Lie superalgebras are also considered.