On faithfulness of the lifting for Hopf algebras and fusion categories
Name
1704.07855.pdf
Description
Submitted version
Size
286.32 KB
Format
Adobe PDF
Checksum (MD5)
cb8294c6f5e98636c0b5edf06305560a
Author(s)
Etingof, Pavel I
Date Issued
June 2018
Journal
Algebra & Number Theory
Publisher
Mathematical Sciences Publishers
Citation
Etingof, Pavel. "On faithfulness of the lifting for Hopf algebras and fusion categories." Algebra & Number Theory 12, 3 (June 2018): 551–569 © 2018 Mathematical Sciences Publishers
Version
Original manuscript
Abstract
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 p to characteristic zero, showing that, moreover, any isomorphism between such structures can be reduced modulo p. 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 p. Keywords: lifting; Hopf algebra; tensor category; separable
Subjects
Algebra and Number Theory
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.2140/ant.2018.12.551
