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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References
Aikawa, T.: 3-dimensional cohomology of the mod p Steenrod algebra. Math. Scand., 47, 91–115 (1980)
Cohen, F., Moore, J., Neisendorfer, J.: The double suspension and exponents of the homotopy groups of spheres. Ann. o. Math., 110, 549–565 (1979)
Liulevicius, A.: The factorizations of cyclic reduced powers by secondary cohomology operations. Mem. Amer. Math. Soc., 42, (1962)
May, J. P.: The Cohomology of Restricted Lie Algebras and of Hopf Algebras, PhD Thesis, Princeton, 1964
May, J. P.: The cohomology of restricted Lie algebras and of Hopf algebras. J. Algebra, 3, 123–146 (1966)
Milnor, J., Moore, J. C.: On the structure of Hopf algebra. Ann. o. Math., 81, 211–264 (1965)
Nave, L. S.: The Smith–Toda complex V ((p + 1)/2) does not exist. Ann. o. Math., 171, 491–509 (2010)
Ravenel, D. C.: Complex Cobordism and Stable Homotopy Groups of Spheres, Academic Press, Orlando, 1986
Toda, H.: On spectra realizing exterior parts of the Steenrod algebra. Topology, 10, 53–65 (1971)
Yu, H. B., Shen, W. H., Zhao, H.: Convergence of the generators of H*,*(U(L)). Southeast Asian Bull. Math., 35, 185–190 (2011)
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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