Cohomology of the Universal Enveloping Algebras of Certain Bigraded Lie Algebras  

作　　者：Li Nan ZHONG Hao ZHAO Wen Huai SHEN 

机构地区：[1]School of Mathematical Sciences, South China Normal University, Guangzhou 510631, P. R. China [2]Department of Mathematics, Yanbian University, Yanji 133000, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2018年第10期1611-1625,共15页数学学报（英文版）

基　　金：supported by NSFC(Grant Nos.11671154 and 11761072);General Financial Grant from the China Postdoctoral Science Foundation(Grant No.2017M622721)

摘　　要：Let p be an odd prime and q = 2（p- 1）. Up to total degree t - s 〈 max（（5p^3 ＋ 6p^2 ＋6p ＋4）q- 10,p^4q}, the generators of H^s,t（U（L））, the cohomology of the universal enveloping algebra of a bigraded Lie algebra L, are determined and their convergence is also verified. Furthermore our results reveal that this cohomology satisfies an analogous Poindare duality property. This largely generalizes an earlier classical results due to J. P. May.Let p be an odd prime and q = 2（p- 1）. Up to total degree t - s 〈 max（（5p^3 ＋ 6p^2 ＋6p ＋4）q- 10,p^4q}, the generators of H^s,t（U（L））, the cohomology of the universal enveloping algebra of a bigraded Lie algebra L, are determined and their convergence is also verified. Furthermore our results reveal that this cohomology satisfies an analogous Poindare duality property. This largely generalizes an earlier classical results due to J. P. May.

关 键 词：Steenrod algebra Hopf algebra Lie algebra spectral sequence stable homotopy groups of sphere 

分 类 号：O152.5[理学—数学] O189.23[理学—基础数学]