Tannakian formalism for topological Hopf algebras

Question

Tannaka-Krein duality allows, under the appropriate assumptions, to reconstruct a Hopf algebra from its category of modules. This method was found to be powerful for instance in the work of Etingof-Kazhdan on quantization of Lie bialgebras.

Briefly, the coproduct of a Hopf algebra $H$ (say, in vector spaces $Vect_{\mathbb{K}}$) defines a symmetric monoidal structure on its category of modules $Mod_H$. We have a forgetful functor $U:Mod_H\rightarrow Vect_{\mathbb{K}}$ called the fiber functor, so that if $U$ is equipped with a symmetric monoidal structure, then one can recover $H$ via an isomorphism $H\cong End(U)$ (the linear endomorphisms of $U$).

My question is the following: is there a Tannaka duality for topological Hopf algebras, e.g. Hopf algebras in Fréchet spaces, Banach spaces, etc...(equipped with the appropriate tensor product) ? If so, what are the main results and good references about this ?

This post imported from StackExchange MathOverflow at 2014-09-29 17:29 (UTC), posted by SE-user Sinan Yalin

Comments

See ncatlab.org/nlab/show/Tannaka+duality . It works for any monoid in nice enough categories. I do not know enough about the particular categories you want to know if they are well behaved enough for the usual arguments to carry through.

This post imported from StackExchange MathOverflow at 2014-09-29 17:29 (UTC), posted by SE-user zibadawa timmy