Cohomology of the Universal Enveloping Algebras of Certain Bigraded Lie Algebras

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 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 Poinćare duality property. This largely generalizes an earlier classical results due to J. P. May.