Cotorsion pairs in cluster categories of type \(A_\infty^\infty\). (English) Zbl 1401.18032
Summary: In this paper, we give a complete classification of cotorsion pairs in a cluster category \(\mathcal{C}\) of type \(A_\infty^\infty\) via certain configurations of arcs, called \(\tau\)-compact Ptolemy diagrams, in an infinite strip with marked points. As applications, we classify \(t\)-structures and functorially finite rigid subcategories in \(\mathcal{C}\), respectively. We also deduce Liu-Paquette’s classification of cluster tilting subcategories of \(\mathcal{C}\) and Ng’s classification of torsion pairs in the cluster category of type \(A_\infty\).
MSC:
| 18E30 | Derived categories, triangulated categories (MSC2010) |
| 16E99 | Homological methods in associative algebras |
Keywords:
cluster category of type \(A_\infty^\infty\); (co)torsion pair; \(\tau\)-compact Ptolemy diagram; \(t\)-structure; cluster tilting subcategoryReferences:
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