Compacte quantum groupen

Martijn Caspers

At the end of the 1980's S.L. Woronowicz stated a definition of a quantum group using a C*-algebraic approach. Until then quantum group structures where mainly studied in an algebraic setting. Woronowicz' definition made a link between quantum groups and analysis, operator algebras and non-commutative geometry.

Using the example of SUq(2) (the quantum SU(2) group), I will introduce the notion of a C*-algebraic compact quantum group. We will see some interesting properties of this structure and define corepresentations and Haar-measures. We give relations between these definitions and their `classical' analogues from group theory. We will also look at relations between corepresentations and the Haar measure. If time permits, I will introduce the notion of a Von Neumann-algebraic locally compact quantum group as was later introduced by S. Vaes and J. Kustermans.

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