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arXiv · 1407.0619

Periodic trees and semi-invariants

Kiyoshi Igusa·Gordana Todorov·Jerzy Weyman
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Abstract

Periodic trees are combinatorial structures which are in bijection with cluster tilting objects in cluster categories of affine type $\tilde{A}_{n-1}$. The internal edges of the tree encode the $c$-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.

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Kiyoshi Igusa, Gordana Todorov, Jerzy Weyman. 2014-07-02. Periodic trees and semi-invariants. https://arxiv.org/abs/1407.0619

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