Conventions -- Universal central extensions. Central trick -- Degenerate sums. The extension r : -- The action ร{130}d. Structure of g*Z, g*R -- Admissible lattices and the category LV. ?-connected components -- The G-module ker ? -- G-invariant [p]-structures -- The extension ? : G* ? G -- Extensions of G by a G-module -- The hochschild groups -- The existence of ? : G* ? G -- Relations in the open cell -- Representatives in G* of the Weyl group -- The theorem of generators and relations and its consequences -- The group functor G*