Quantum groups with invariant integrals (Q2730674)

In this survey paper the author explains some notions related to multiplier Hopf \(*\)-algebras, which he introduced [in Trans. Am. Math. Soc. 342, No. 2, 917-932 (1994; Zbl 0809.16047)], generalizing the notion of Hopf algebra, and their connection with the quantization of non-compact groups. In this context, he discusses various aspects of the notion of an integral or ``Haar measure'' and formulates a duality for multiplier Hopf \(*\)-algebras with an integral. The last section of the paper presents an example that serves to illustrate the material exposed before.NEWLINENEWLINENEWLINEThe author points out in the introduction that the point of view of this paper can be seen as a model for a more general operator algebra approach to quantum groups as treated by \textit{J. Kustermans} and \textit{S. Vaes} [in Proc. Natl. Acad. Sci. USA 97, No. 2, 547-552 (2000; Zbl 0978.46044)].