Hochschild and cyclic homology of quantum groups

For an arbitrary complex linear semisimple Lie groupG, we consider Hopf algebras of the deformations of the formal and algebraic functions onG. The Hochschild and cyclic homology of these Hopf algebras are computed when the value of the deformation parameter is generic.The main result of this paper was announced at the AMS meeting at University Park in April 1990Supported by Department of Energy under Grant DE-FG02-88ER25062Supported by Harvard Prize Fellowship. Address after July, 1990: Department of Mathematics, Pennsylvania State University, University Park, PA 16802, USA