Cohomology of Quantum General Linear Groups,

This paper deals with the cohomology of infinitesimal quantum general linear groups. We prove that Hodd((Gq)1, K) = 0 and Hev((Gq)1, K) K[ ]. Our approach is to consider theq-analogue of a unipotent group scheme and construct a filtration of the Hochschild complex forK[(Uq)1]. Meanwhile a certainq-deformation of a polynomial coalgebra arises naturally, which is also believed to be interesting.