Let $H$ be a semisimple Hopf algebra over an algebraically closed field of characteristic zero. Further, let $K\subseteq H$ be a normal Hopf subalgebra. As we all know, $H$ then can be reconstructed from $K$ by some compatible data [1].

I want to know if there exists a similar result on Rep($H$) and Rep($K$), where Rep($H$) is the fusion category of finite-dimensional representations of $H$? If not, what can be said about Rep($H$) and Rep($K$)?

Thank you!

[1]N. Andruskiewitsch, Notes on extensions of Hopf algebras, Canad. J. Math. 48 (1996), 3-42


The following article may interest you: C. Pinzari and J. Roberts, A Duality Theorem for Ergodic Actions of Compact Quantum Groups on C *-Algebras, Communications in Mathematical Physics 277 (2008) no 2, 385-421.

However, this article is written in the language of C*-tensor categories and compact quantum groups.

I hope this helps...


Your Answer

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Not the answer you're looking for? Browse other questions tagged or ask your own question.