Abstract

The material in this chapter is related, directly or indirectly, to the corepresentation theory of Hopf algebras. In Sects. 11.2 and 11.3 we investigate two classes of Hopf algebras resp. Hopf ∗-algebras, called cosemisimple Hopf algebras resp. compact quantum group algebras, which are determined by their irreducible resp. unitary corepresentations. The second class leads at once to Woronowicz’ compact quantum group C*-algebras studied in Sect. 11.4. In Sect. 11.5 the irreducible representations of the quantum group GL q (N) when q is not a root of unity are classified. The final Sect. 11.6 gives an introduction to, quantum homogeneous spaces.

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