Amenability and Co-Amenability of Algebraic Quantum Groups II

We continue our study of the concepts of amenability and co-amenability for algebraic quantum groups in the sense of A. Van Daele and our investigation of their relationship with nuclearity and injectivity. One major tool for our analysis is that every non-degenerate *-representation of the universal C*-algebra associated to an algebraic quantum group has a unitary generator which may be described in a concrete way. Subj. Class.: Ouantum groups, C*-algebras MSC 2000: Primary 46L05, 46L65. Secondary 16W30, 22D25, 58B32. Keywords: quantum group, amenability, nuclearity, injectivity.