• Register
PhysicsOverflow is a next-generation academic platform for physicists and astronomers, including a community peer review system and a postgraduate-level discussion forum analogous to MathOverflow.

Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.

Please help promote PhysicsOverflow ads elsewhere if you like it.


PO is now at the Physics Department of Bielefeld University!

New printer friendly PO pages!

Migration to Bielefeld University was successful!

Please vote for this year's PhysicsOverflow ads!

Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!

... see more

Tools for paper authors

Submit paper
Claim Paper Authorship

Tools for SE users

Search User
Reclaim SE Account
Request Account Merger
Nativise imported posts
Claim post (deleted users)
Import SE post

Users whose questions have been imported from Physics Stack Exchange, Theoretical Physics Stack Exchange, or any other Stack Exchange site are kindly requested to reclaim their account and not to register as a new user.

Public \(\beta\) tools

Report a bug with a feature
Request a new functionality
404 page design
Send feedback


(propose a free ad)

Site Statistics

205 submissions , 163 unreviewed
5,047 questions , 2,200 unanswered
5,345 answers , 22,709 comments
1,470 users with positive rep
816 active unimported users
More ...

  Tannakian formalism for topological Hopf algebras

+ 4 like - 0 dislike

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
asked Sep 25, 2014 in Theoretical Physics by Sinan Yalin (20 points) [ no revision ]
retagged Sep 29, 2014
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

Your answer

Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
Please consult the FAQ for as to how to format your post.
This is the answer box; if you want to write a comment instead, please use the 'add comment' button.
Live preview (may slow down editor)   Preview
Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:
Then drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds).
Please complete the anti-spam verification

user contributions licensed under cc by-sa 3.0 with attribution required

Your rights