Faculty of Mathematics
Collaborative Research Centre 701
Spectral Structures and Topological Methods in Mathematics

# Project C3

## Topological and spectral structures in representation theory

Principal Investigator(s) Other Investigators

## Summary:

We will continue to study the representations of finite-dimensional associative algebras as they arise in many parts of mathematics and mathematical physics. The main target will be to describe the general structure of the module category, its derived categories as well as related categories, in particular the homotopy category of perfect complexes. Combinatorial invariants lead to topological structures such as the Auslander-Reiten complex, the geometrical analysis deals with the spectral parameters involved.

 13012 Abelian length categories of strongly unbounded type PDF | PS.GZ 13004 The Auslander bijections: How morphisms are determined by modules PDF | PS.GZ 12138 Quantum cluster algebras of type A and the dual canonical basis PDF | PS.GZ 12137 Acyclic cluster algebras from a ring theoretic point of view PDF | PS.GZ 12134 Cotorsion pairs and t-structures in a 2-Calabi-Yau triangulated category PDF | PS.GZ 12133 $\tau$-rigid modules for algebras with radical square zero PDF | PS.GZ 12127 From submodule categories to preprojective algebras PDF | PS.GZ 12119 Distinguished bases of exceptional modules PDF | PS.GZ 12082 Cohomological length functions PDF | PS.GZ 12068 The Gorenstein projective modules for the Nakayama algebras PDF | PS.GZ