Cluster categories and their relation to cluster algebras, semi-invariants and homology of torsion free nilpotent groups

摘要

The structure of cluster categories [BMRRT] is well suited for the combinatorics of cluster algebras [FZ1] with the main correspondence being between tilting objects and clusters. Furthermore it was shown in [IOTW] that there is a close relation between domains of virtual semi-invariants and simplicial complexes asso ciated to cluster categories. Also the same simplicial complexes associated to cluster categories are related to the Igusa-Orr pictures in the homology of nilpotent groups