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arXiv · 1601.00314

Periodicity of cluster tilting objects

Benedikte Grimeland
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Abstract

Let T be a locally finite triangulated category with an autoequivalence F such that the orbit category T/F is triangulated. We show that if X is an m-cluster tilting subcategory, then the image of X in T/F is an m-cluster tilting subcategory if and only if X is F-perodic. We show that for path-algebras of Dynking quivers δone may study the periodic properties of n-cluster tilting objects in the n-cluster category Cn(kδ) to obtain information on periodicity of the preimage as n-cluster tilting subcategories of Db(kδ). Finally we classify the periodic properties of all 2-cluster tilting objects T of Dynkin quivers, in terms of symmetric properties of the quivers of the corresponding cluster tilted algebras EndC_2(T)^op. This gives a complete overview of all 2-cluster tilting objects of all triangulated orbit categories of Dynkin diagrams.

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Benedikte Grimeland. 2016-01-03. Periodicity of cluster tilting objects. https://arxiv.org/abs/1601.00314

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