As far as I know, low-dimensional semisimple Hopf algebras are classified (along with non-semisimple ones) up to dimension 60, with the first example of a semisimple Hopf algebra not coming from a finite group in dimension 8.

How well are low-dimensional Hopf superalgebras, that is, $\mathbb{Z}_2$-graded Hopf algebras or Hopf algebra objects internal to $\mathbb{Z}_2-\operatorname{Vect}$ understood? Up to which dimension are they classified? Are there interesting semisimple ones? Has someone worked out the representations? I could find an article on the classification of finite dimensional ones up to dimension 4, but it didn't mention semisimplicity or higher dimensional semisimple examples.

Generally, how well are low-dimensional semisimple braided Hopf algebras (internal to a braided category) understood?


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.

Browse other questions tagged or ask your own question.