Locally compact quantum groups in the universal setting

Details Locally compact quantum groups in the universal setting Locally compact quantum groups in the universal setting

1999-02-02

arxiv.org/abs/math/9902015v1

Mathematics

Operator Algebras

37 pages, LaTeX

Scientific paper

In this paper we associate to every reduced C*-algebraic quantum group A a universal C*-algebraic quantum group. We fine tune a proof of Kirchberg to show that every *-representation of a modified L1-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 uinversal C*-algebra. We show that this universal C*-algebra carries a quantum group structure which is as rich as its reduced companion.

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