The ramifications of the centres: quantised function algebras at roots of unity

Abstract

Let H be a Hopf algebra which is a finite module over a central sub-Hopf algebra R. We continue the study of such algebras begun in RT/9911234, concentrating in this case on the example of $O_{\epsilon}[G]$, a quantised function algebra at root of unity. In particular we determine the representation type and block structure of the family of reduced quantised function algebras, and describe many of them up to isomorphism. A series of parallel results is obtained for the quantised Borel algebras $U_{\epsilon}^{\geq 0}$.