Multiplier Hopf algebras and duality

摘要: We define a category containing the discrete quantum groups (and hence and duals of compact groups) groups). The dual an object can be defined within same we have biduality theorem. This theory extends duality between one abelian objects in our are multiplier Hopf algebras, with invertible antipode, admitting invariant functionals (integrals), satisfying some extra condition (to take care non-abelianness underlying algebras). If start ∗-algebra positive functionals, then also is functionals. makes it possible to formulate this framework C∗-algebras.