Coloured quiver mutation for higher cluster categories

2008/09/03 by Aslak Bakke Buan, Hugh Thomas, Buan, Aslak Bakke +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.0809.0691

openalex publication_date 2008/09/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define mutation on coloured quivers associated to tilting objects in higher cluster categories. We show that this operation is compatible with the mutation operation on the tilting objects. This gives a combinatorial approach to tilting in higher cluster categories and especially an algorithm to determine the Gabriel quivers of tilting objects in such categories.

Citations

• On triangulated orbit categories

Cited by

• An explicit description of the colored mutation class of \widetilde\mathbbA_n-quivers

Related

• Graded mutation in cluster categories coming from hereditary categories with a tilting object
• Finite mutation classes of coloured quivers
• A geometric realization of the m-cluster categories of type D_n
• A combinatorial procedure for tilting mutation
• Cluster mutation via quiver representations