Ordinary Hopf Algebra Research Articles

Braided groups

We prove a highly generalized Tannaka-Krein type reconstruction theorem for a monoidal category C functored by F: C→ V to a suitably cocomplete rigid quasitensor category V . The generalized theorem associates to this a bialgebra or Hopf algebra Aut( C , F, V ) in the category V . As a corollary, to every cocompleted rigid quasitensor category C is associated Aut ( C)=Aut( C, id, C ̄ ) . It is braided-commutative in a certain sense and hence analogous to the ring of ‘co-ordinate functions’ on a group or supergroup, i.e., a ‘braided group’. We derive the formulae for the transmutation of an ordinary dual quasitriangular Hopf algebra into such a braided group. More generally, we obtain a Hopf algebra B( A 1, ƒ, A 2) (in a braided category) associated to an ordinary Hopf algebra map ƒ : A 1→ A 2 between ordinary dual quasitriangular Hopf algebras A 1, A 2.