A Characterization for Discrete Quantum Group - doi: 10.5269/bspm.v23i1-2.7455

Abstract

Based on the work of A.Van Daele, E.G.Effros and Z.J.Ruan on multiplier Hopf algerba and discrete quantum group, this paper states that discrete quantum group (A, \Delta) is exactly the set {(\omega \otimes \iota) \Delta(a) | a\in A, \omega \in A^{\ast}}, where A^{\ast} is the space of all reduced functionals on A.Furthermore, this paper characterizes (A, \Delta) as an algebraic quantum group with a standard \ast-operation and a special element z \in  A such that (1 \otimes ­ a) \Delta(z) = \Delta(z)(a ­ \otimes 1) (\forall a \in A).