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Algebraic quantum hypergroups. (English) Zbl 1206.43004
In the paper under review the authors show that many of the nice aspects of the duality for algebraic quantum groups remain valid if one considers (not necessarily finite dimensional) Hopf-like algebras in which the comultiplication is no longer assumed to be an algebra homomorphism (the existence of a left and a right integral and of a properly defined antipod is still required). Such objects are called algebraic quantum hypergroups. For algebraic quantum hypergroups the authors establish a duality theory much along the same lines as for algebraic quantum groups. Further, the authors define algebraic quantum hypergroups of compact type and discrete type and show that these types are dual to each other. Several examples illustrating different aspects of the theory are given.

MSC:
43A62 Harmonic analysis on hypergroups
20G42 Quantum groups (quantized function algebras) and their representations
17B37 Quantum groups (quantized enveloping algebras) and related deformations
81R50 Quantum groups and related algebraic methods applied to problems in quantum theory
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