7 papers
Algebras in fusion categories: species and hereditary algebras
Edmund Heng, Mateusz StroiÅski
We initiate the study of non-semisimple algebras in fusion categories by establishing the framework of -species -- analogous to the framework of species and quivers us…
Coxeter planes as fixed points of Verlinde fusion rings
Max Boyle, Edmund Heng
For the Coxeter groups of ADE type, we provide a construction of their Coxeter planes as fixed points of actions of hypergroups associated to Verlinde fusion rings. This builds upo…
Representations of Coxeter groups over fusion rings and hyperplane complements
Edmund Heng, Luis Paris
We study faithful realisations of Coxeter groups over fusion rings and study Vinberg systems associated to them. We show that they induce embeddings of hyperplane complements, whic…
Normalisers of parabolic subgroups of Artin--Tits groups and Tits cone intersections
Owen Garnier, Edmund Heng, Anthony Licata +1
Let be a Coxeter diagram and let . Motivated by 3-fold flops, Iyama and Wemyss study the hyperplane arrangement in the Tits cone intersection of , which is…
Periodic elements in finite type Artin-Tits groups and stability conditions
Edmund Heng, Anthony M. Licata, Oded Yacobi
Periodic elements in finite type Artin--Tits groups are elements some positive power of which is central. We give a dynamical characterisation of periodic elements via their action…
Stability conditions and Artin--Tits groups
Edmund Heng, Anthony M. Licata
We describe spaces of Bridgeland stability conditions on certain triangulated categories associated to Coxeter systems. These categories are defined algebraically using the categor…