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2008

New Graphs of Finite Mutation Type

Derksen, Harm, Owen, Theodore

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To a directed graph without loops and 2-cycles, we can associate a skew-symmetric matrix with integer entries.

Mutations of such skew-symmetric matrices, and more generally skew-symmetrizable matrices, have been defined in the context of cluster algebras by Fomin and Zelevinsky.
The mutation class of a graph G is the set of all isomorphism classes of graphs that can be obtained from G by a sequence of mutations.
A graph is called mutation-finite if its mutation class is finite.

New Graphs of Finite Mutation Type · Around

Built on

K. Saito, Extended affine root systems. I. Coxeter transformations
Original
1985
Earlier work this paper cites.
S. Fomin, A. Zelevinsky, Cluster algebras I: Foundations
2002
Earlier work this paper cites.
S. Fomin, A. Zelevinsky, Cluster algebras II: Finite type classification
2003
Earlier work this paper cites.

Similar

A. Berenstein, S. Fomin, A. Zelevinsky, Cluster algebras. III. Upper bounds and double Bruhat cells
2005
Cited alongside, same era.
C. Geiss, B. Leclerc, J. Schröer, Semicanonical bases and preprojective algebras
2005
Cited alongside, same era.
I. Assem, M. Blais, Th. Brüstle, A. Samson, Mutation classes of skew-symmetric 3 × 3 3\times 3 matrices
Cited in the paper.
S. Fomin, M. Shapiro, D. Thurston, cluster algebras and triangulated surfaces part I: cluster complexes
Cited in the paper.
B. Keller, Quiver mutation in Java, http://www.math.jussieu.fr/
Cited in the paper.

Then

A. B. Buan, I. Reiten, Acyclic quivers of finite mutation type
2006
Later among the works it cites.
S. Fomin, A. Zelevinsky, Cluster algebras IV: Coefficients
2007
Later among the works it cites.

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