Cluster categories and torsion theory

• Applicant: Professor Dr. Thorsten Holm
• Subject Area: Mathematics
• Term: from 2012 to 2015
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 219520929

Cluster categories form a categorification of Fomin and Zelevinsky’s cluster algebras, a topic linking diverse mathematical areas in unexpected ways. In the proposed project we plan to study the structure of cluster categories and their higher generalisations, the d-cluster categories. Torsion theory is fundamental in the representation theory of algebras and recently also for triangulated categories. A particular focus of the project will be on classifications of torsion pairs in cluster categories, in particular for cluster categories attached to cluster algebras coming from triangulations of surfaces. Along the way, interesting special cases, e.g. Dynkin and extended Dynkin types, might already present challenging problems. Moreover, we plan to examine cluster behaviour in triangulated categories with Auslander-Reiten quiver of infinite Dynkin type, and to classify their (weak) cluster tilting subcategories. To this end, topological/geometric models for such categories would be useful which allow explicit calculations. We also plan to find geometric realisations of such categories ’in nature’.

• DFG Programme: Priority Programmes
• Subproject of: SPP 1388: Representation Theory