A coassociativeC*-quantum group with nonintegral dimensions
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By weakening the counit and antipode axioms of aC*-Hopf algebra and allowing for the coassociative coproduct to be nonunital, we obtain a quantum group, that we call aweak C*-Hopf algebra, which is sufficiently general to describe the symmetries of essentially arbitrary fusion rules. This amounts to generalizing the Baaj-Skandalis multiplicative unitaries to multipicative partial isometries. Every finite-dimensional weakC*-Hopf algebra has a dual which is again a weakC*-Hopf algebra. An explicit example is presented with Lee-Yang fusion rules. We briefly discuss applications to amalgamated crossed products, doubles, and quantum chains.
Mathematics Subject Classification (1991)81R50
Key wordsWeak Hopf algebras multiplicative isometries amalgamated crossed products
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