Generalized P(N)-graded Lie superalgebras  

作　　者：Jin CHENG Yun GAO 

机构地区：[1]School of Mathematics and Statistics,Shandong Normal University,Jinan,250014,China [2]Department of Mathematics and Statistics,York University,Toronto,ON,M3J 1P3,Canada

出　　处：《Frontiers of Mathematics in China》2021年第3期647-687,共41页中国高等学校学术文摘·数学（英文）

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

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

关 键 词：Root system graded Lie superalgebras associative superalgebra quantum tori REPRESENTATIONS 

分 类 号：O151[理学—数学]