Compact Quantum Groupoids

Abstract

Quantum groupoids are a joint generalization of groupoids and quantum groups. We propose a definition of a compact quantum groupoid that is based on the theory of C*-algebras and Hilbert bimodules. The essential point is that whenever one has a tensor product over the complex numbers in the theory of quantum groups, one now uses a certain tensor product over the base algebra of the quantum groupoid.Comment: 8 pages, to appear in `Quantum Theory and Symmetries' (Goslar, 18-22 July 1999), eds. H.-D. Doebner et a