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