Acta Mathematica Sinica, English Series

, Volume 34, Issue 10, pp 1611–1625 | Cite as

Cohomology of the Universal Enveloping Algebras of Certain Bigraded Lie Algebras

  • Li Nan Zhong
  • Hao ZhaoEmail author
  • Wen Huai Shen


Let p be an odd prime and q = 2(p−1). Up to total degree t−s < max{(5p3 +6p2 +6p+ 4)q − 10, p4q}, the generators of Hs,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 Poinćare duality property. This largely generalizes an earlier classical results due to J. P. May.


Steenrod algebra Hopf algebra Lie algebra spectral sequence stable homotopy groups of sphere 

MR(2010) Subject Classification

55Q45 55S10 17B35 


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Copyright information

© Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematical SciencesSouth China Normal UniversityGuangzhouPR China
  2. 2.Department of MathematicsYanbian UniversityYanjiPR China

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