Locally compact quantum groups in the universal setting

  title={Locally compact quantum groups in the universal setting},
  author={Johan Kustermans},
In this paper we associate to every reduced C∗-algebraic quantum group (A,∆) (as defined in [18]) a universal C∗-algebraic quantum group (Au, ∆u). We fine tune a proof of Kirchberg to show that every ∗-representation of a modified L-space is generated by a unitary corepresentation. By taking the universal enveloping C∗-algebra of a dense sub ∗-algebra of A we arrive at the C∗-algebra Au. We show that this C∗-algebra Au carries a quantum group structure which is as rich as its reduced companion… CONTINUE READING
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