We use a version of Haboush’s theorem over complete local Noetherian rings to
prove faithfulness of the lifting for semisimple cosemisimple Hopf algebras
and separable (braided, symmetric) fusion categories from characteristic
to characteristic
zero, showing that, moreover, any isomorphism between such structures can be reduced
modulo
.
This fills a gap in our earlier work. We also show that lifting of semisimple
cosemisimple Hopf algebras is a fully faithful functor, and prove that
lifting induces an isomorphism on Picard and Brauer–Picard groups.
Finally, we show that a subcategory or quotient category of a separable
multifusion category is separable (resolving an open question from our earlier
work), and use this to show that certain classes of tensor functors between
lifts of separable categories to characteristic zero can be reduced modulo
.
To Alexander Kirillov, Jr. on his 50th
birthday with admiration
PDF Access Denied
We have not been able to recognize your IP address
44.200.168.16
as that of a subscriber to this journal.
Online access to the content of recent issues is by
subscription, or purchase of single articles.
Please contact your institution's librarian suggesting a subscription, for example by using our
journal-recommendation form.
Or, visit our
subscription page
for instructions on purchasing a subscription.
