Generalized P(N)-graded Lie superalgebras

作     者：Jin CHENG Yun GAO Jin CHENG;Yun GAO

作者机构：School of Mathematics and StatisticsShandong Normal UniversityJinan250014China Department of Mathematics and StatisticsYork UniversityTorontoONM3J 1P3Canada 

出 版 物：《Frontiers of Mathematics in China》 (中国高等学校学术文摘·数学（英文）)

年 卷 期：2021年第16卷第3期

页      面：647-687页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：This work was supported by the National Natural Science Foundation of China(Grant Nos.11701340 11931009)and the NSERC of Canada 

主　　题：Root system graded Lie superalgebras associative superalgebra quantum tori representations 

摘      要：We generalize the P(N)-graded Lie superalgebras of *** generalization is not so restrictive but sufficient enough so that we are able to have a classification for this generalized P(N)-graded Lie *** result is that the generalized P(N)-graded Lie superalgebra L is centrally isogenous to a matrix Lie superalgebra coordinated by an associative superalgebra with a ***,L is P(N)-graded if and only if the coordinate algebra R is commutative and the super-involution is *** recovers Martinez-Zelmanov’s theorem for type P(N).We also obtain a generalization of Kac’s coordinatization via Tits-Kantor-Koecher ***,the motivation of this generalization comes from the Fermionic-Bosonic module construction.