The Cluster Category

This is a kind of universal object CA
for all the module categories
of cluster tilted algebras C(End T),
where T is a tilting A-module.

It was introduced by
Buan-Marsh-Reineke-Reiten-Todorov.

 

CA is the orbit category of the derived category Db(mod A) for the functor τ-1[1].

Keller has shown: CA is a triangulated category.

If T is a tilting A-module, then mod C(End T) = CA/T.


The left picture shows the embedding of mod A into CA, the right picture concerns the case when T is a regular A-module.