Mutation of torsion pairs in triangulated categories and its geometric realization

2011/05/18 by Yu Zhou, Bin Zhu, Zhou, Yu +1 · 2 citations
Mathematics · Physics and Astronomy · #05A15 #13F60 #16G20 #16G70 #18E30 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1105.3521

openalex publication_date 2011/05/18 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We introduce and study mutation of torsion pairs, as a generalization of mutation of cluster tilting objects, rigid objects and maximal rigid objects. It is proved that any mutation of a torsion pair is again a torsion pair. A geometric realization of mutation of torsion pairs in the cluster category of type A_n or A_∞ is given via rotation of Ptolemy diagrams.

Citations

• On triangulated orbit categories

Cited by

• Mutation of n-cotorsion pairs in extriangulated categories
• Cluster subalgebras and cotorsion pairs in Frobenius extriangulated categories

Related

• Mutation of n-cotorsion pairs in triangulated categories
• Torsion pairs in finite 2-Calabi-Yau triangulated categories with maximal rigid objects
• Triangulated structures induced by mutations
• Torsion pairs in repetitive cluster categories of type A_n
• Mutation and torsion pairs