Cluster subalgebras and cotorsion pairs in Frobenius extriangulated categories

Wen Chang Shaanxi Normal University Panyue Zhou Tsinghua University Bin Zhu Tsinghua University

Category Theory mathscidoc:1610.04002

Nakaoka and Palu introduced the notion of extriangulated categories by extracting the similarities between exact categories and triangulated categories. In this paper, we study cotorsion pairs in a Frobenius extriangulated category $\C$. Especially, for a $2$-Calabi-Yau extriangulated category $\C$ with a cluster structure, we describe the cluster substructure in the cotorsion pairs. For rooted cluster algebras arising from $\C$ with cluster tilting objects, we give a one-to-one correspondence between cotorsion pairs in $\C$ and certain pairs of their rooted cluster subalgebras which we call complete pairs. Finally, we explain this correspondence by an example relating to a Grassmannian cluster algebra.
Frobenius extriangulated categories; 2-Calabi-Yau extriangulated (or triangulated) categories; Cotorsion pairs; Cluster algebras
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@inproceedings{wencluster,
  title={Cluster subalgebras and cotorsion pairs in Frobenius extriangulated categories},
  author={Wen Chang, Panyue Zhou, and Bin Zhu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161017163542890893205},
}
Wen Chang, Panyue Zhou, and Bin Zhu. Cluster subalgebras and cotorsion pairs in Frobenius extriangulated categories. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161017163542890893205.
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