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Cluster categories and duplicated algebras

Ibrahim Assem·Thomas Brüstle·Ralf Schiffler·Gordana Todorov
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Abstract

Let $A$ be a hereditary algebra. We construct a fundamental domain for the cluster category of $A$ inside the category of modules over the duplicated algebra $\bar{A}$ of $A$. We then prove that there exists a bijection between the tilting objects in the cluster category and the tilting $\bar{A}$-modules all of whose non projective-injective indecomposable summands lie in the left part of the module category of $\bar{A}$.

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Ibrahim Assem, Thomas Brüstle, Ralf Schiffler, Gordana Todorov. 2005-09-21. Cluster categories and duplicated algebras. https://arxiv.org/abs/math/0509501

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