Cohomology of quantum general linear groups (Q1282346)

The author considers the cohomology of infinitesimal quantum general linear groups. He shows that \(H^{odd}((G_q)_1, K)=0\) and \(H^{ev}((G_q)_1, K)=K[\mathcal N]\). The method he uses is to consider the \(q\)-analog of the coordinate algebra for the infinitesimal unipotent group, i.e. \(K[(U_q)_1]\). Using a filtration of the Hochschild complex for \(K[(U_q)_1]\), he relates the cohomology of \(K[(U_q)_1]\) to (via a spectral sequence) the cohomology of a certain \(q\)-deformation of a infinitesimal polynomial coalgebra, which is computable.