Coloured quiver mutation for higher cluster categories
By Aslak Bakke Buan, Hugh Thomas. 2008
47 citations recorded by the source corpus.
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.
Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/c5cd0a6d33ac3e573db860aff689b4528f6db810
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Algebra and Number Theory
In Geometry and Topology
In Statistical and Nonlinear Physics
Citations in the corpus
- Cluster categories (2010, background): “It was shown in [29] that also for arbitrarym there is a combinatorial description of mutation of m-cluster tilting objects in m-cluster categories.”
- Exchange graphs and Ext quivers (2011, methodology): “For our second main result (Theorem 8.10), we exploit this circle of identifications to interpret the coloured quiver of Buan-Thomas [8], which is associated to any cluster tilting set Y = α ( H ) in CEG N − 1 ( Q ), in terms of the Ext quiver of any heart H in the corresponding Br-orbit in EG ◦ (Γ N”
- Cluster tilting for higher Auslander algebras (2008, background): “There are a lot of recent work on higher cluster tilting [ABST, BaM, BT , EH, HZ1, HZ2, HZ3, JH1, JH2, L, T, W, Z, ZZ].”