Mathematics – Operator Algebras
Scientific paper
2000-05-23
Mathematica Scandinavica 92 (1) (2003), 68--92.
Mathematics
Operator Algebras
19 pages, LaTeX2e file
Scientific paper
In this paper we complete in several aspects the picture of locally compact quantum groups. First of all we give a definition of a locally compact quantum group in the von Neumann algebraic setting and show how to deduce from it a C*-algebraic quantum group. Further we prove several results about locally compact quantum groups which are important for applications, but were not yet settled in our paper "Locally compact quantum groups". We prove a serious strengthening of the left invariance of the Haar weight, and we give several formulas connecting the locally compact quantum group with its dual. Loosely speaking we show how the antipode of the locally compact quantum group determines the modular group and modular conjugation of the dual locally compact quantum group.
Kustermans Johan
Vaes Stefaan
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