%0 Journal Article
%T A Coassociative C*-Quantum Group with Non-Integral Dimensions
%A G. Bohm
%A K. Szlachanyi
%J Mathematics
%D 1995
%I arXiv
%R 10.1007/BF01815526
%X By weakening the counit and antipode axioms of a C*-Hopf algebra and allowing for the coassociative coproduct to be non-unital we obtain a quantum group, that we call a weak 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 weak C*-Hopf algebra has a dual which is again a weak C*-Hopf algebra. An explicit example is presented with Lee-Yang fusion rules. We shortly discuss applications to amalgamated crossed products, doubles, and quantum chains.
%U http://arxiv.org/abs/q-alg/9509008v1