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arXiv · 1610.05006

Cluster subalgebras and cotorsion pairs in Frobenius extriangulated categories

Wen Chang·Panyue Zhou·Bin Zhu
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Abstract

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.

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BibTeXRIS

Wen Chang, Panyue Zhou, Bin Zhu. 2016-10-17. Cluster subalgebras and cotorsion pairs in Frobenius extriangulated categories. https://arxiv.org/abs/1610.05006

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