## 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.

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