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A geometric interpretation of the triangulated structure of m-cluster categories
m-cluster categories triangulated structure Auslander-Reiten triangles orbit categories Auslander Reiten quivers
2011/8/25
Abstract: The aim of this note is to answer several open problems arising from the geometric description of the $m$-cluster categories of type $A_n$ and their realization in terms of the $m$-th power ...
Cluster categories were defined in [BMRRT] in order to use categorical methods to give a conceptual model for the combinatorics of cluster algebras, as defined by Fomin and Zelevinsky [FZ].
Cluster categories
Cluster categories
2011/2/25
Cluster algebras were introduced by Fomin-Zelevinsky in 2002 in order to give a combinatorial framework for phenomena occurring in the context of algebraic groups.
Graded mutation in cluster categories coming from hereditary categories with a tilting object
Graded mutation cluster categories hereditary categories tilting object
2010/12/13
We present a graded mutation rule for quivers of clustertilted algebras. Furthermore, we give a technique to recover a clustertilting object from its graded quiver in the cluster category of cohX.