Abstract
Motivated by recent advances in the categorification of quantum groups at prime roots of unity, we develop a theory of 2representations for 2 categories, enriched with a pdifferential, which satisfy finiteness conditions analogous to those of finitary or fiat 2categories. We construct cell 2representations in this setup, and consider a class of 2categories stemming from bimodules over a pdg category in detail. This class is of particular importance in the categorification of quantum groups, which allows us to apply our results to cyclotomic quotients of the categorifications of small quantum group of type sl2 at prime roots of unity by Elias–Qi [Advances in Mathematics 288 (2016)]. Passing to stable 2representations gives a way to construct triangulated 2representations, but our main focus is on working with pdg enriched 2representations that should be seen as a pdg enhancement of these triangulated ones.
Original language  English 

Article number  106937 
Number of pages  66 
Journal  Advances in Mathematics 
Volume  361 
Early online date  31 Dec 2019 
DOIs  
Publication status  Published  12 Feb 2020 
Keywords
 2Representation theory
 Categorification at roots of unity
 Enriched 2categories
 Hopfological algebra
 QUANTUMFIELD THEORY
 SIMPLE TRANSITIVE 2REPRESENTATIONS
Profiles

Vanessa Miemietz
 School of Mathematics  Associate Professor in Pure Mathematics
 Algebra and Combinatorics  Member
Person: Research Group Member, Academic, Teaching & Research