Projects per year
Abstract
Motivated by the socalled Hcell reduction theorems, we investigate certain classes of bicategories which have only one Hcell apart from possibly the identity. We show that H_0simple quasi fiab bicategories with unique Hcell H_0 are fusion categories. We further study two classes of nonsemisimple quasifiab bicategories with a single Hcell apart from the identity. The first is $\cH_A$, indexed by a finitedimensional radically graded basic Hopf algebra A, and the second is $\cG_A$, consisting of symmetric projective AAbimodules. We show that $\cH_A$ can be viewed as a 1full subbicategory of $\cG_A$ and classify simple transitive birepresentations for $\cG_A$. We point out that the number of equivalence classes of the latter is finite, while that for $\cH_A$ is generally not.
Original language  English 

Article number  107328 
Journal  Journal of Pure and Applied Algebra 
Volume  227 
Issue number  7 
Early online date  16 Jan 2023 
DOIs  
Publication status  Published  Jul 2023 
Keywords
 Bicategory
 Hopf algebra
 Symmetric bimodule
Projects
 1 Finished

2representation theory and categorification
Engineering and Physical Sciences Research Council
2/04/19 → 31/03/23
Project: Research