A characterization theorem for cosemisimple quantum groups, Part I

Paddy McCrudden – 11 October 2000

This is joint work with Ross Street and Brian Day It is well-known that the character table does not provide a characterization of compact groups. On the other hand, Tannaka duality shows that a compact group is characterized by its symmetric monoidal category of representations along with the forgetful functor. In this seminar we use a variant of promonoidal categories adapted to free coproduct completions to characterize cosemisimple quantum groups, among which lie compact groups. The data characterizing these algebras is simple combinatorial data: a set along with certain families of complex matrices satisfying various axioms. Such an object we tentatively call a contragroup. In the sequel to this seminar we will provide an explicit calculation of the dual contragroup of the group algebra of the group of symmetries of the triangle.