Cosemisimple Bialgebras and Discrete Quantum Semigroups Original Research Article

We show for a cosemisimple bialgebra that a standard *-operation making it into a discrete quantum semigroup must be unique. It may not exist: we prove such an operation on a cosemisimple imageq(SL2(image)) exists if and only if the parameterqis real. We also conclude that discrete quantum groups form a more restrictive class than cosemisimple *-Hopf algebras.