Periodic trees and semi-invariants
arXiv:1407.0619
Abstract
Periodic trees are combinatorial structures which are in bijection with cluster tilting objects in cluster categories of affine type . The internal edges of the tree encode the -vectors corresponding to the cluster tilting object, as well as the weights of the virtual semi-invariants associated to the cluster tilting object. We also show a direct relationship between the position of the edges of the tree and whether the corresponding summands of the cluster tilting object are preprojective, preinjective or regular.
33 pages, 6 figures