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Cohomology of the Universal Enveloping Algebras of Certain Bigraded Lie Algebras

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Abstract

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.

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Authors and Affiliations

  1. School of Mathematical Sciences, South China Normal University, Guangzhou, 510631, PR China

    Li Nan Zhong, Hao Zhao & Wen Huai Shen

  2. Department of Mathematics, Yanbian University, Yanji, 133000, PR China

    Li Nan Zhong

Authors
  1. Li Nan Zhong
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  2. Hao Zhao
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  3. Wen Huai Shen
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Corresponding author

Correspondence to Hao Zhao.

Additional information

This paper was supported by NSFC (Grant Nos. 11671154 and 11761072) and General Financial Grant from the China Postdoctoral Science Foundation (Grant No. 2017M622721)

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Zhong, L.N., Zhao, H. & Shen, W.H. Cohomology of the Universal Enveloping Algebras of Certain Bigraded Lie Algebras. Acta. Math. Sin.-English Ser. 34, 1611–1625 (2018). https://doi.org/10.1007/s10114-018-7273-9

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  • DOI: https://doi.org/10.1007/s10114-018-7273-9

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