Problems and Perspectives

In (III.10.1)—(III.10.3) we discuss problems concerning the PI Hopf triples of (III.4.1)(1). So throughout these three paragraphs let be a PI Hopf triple over the algebraically closed field k. We then briefly consider more general PI Hopf algebras in (III.10.4), before moving on to more specialised questions about quantized function algebras and quantized enveloping algebras in the remainder of the chapter. In the cases where there has been progress on a question since it was stated in the lectures at Barcelona we have chosen, for the sake of historical accuracy, first to state the question as it was given in the lectures, and then to discuss subsequent developments.