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We derive an algorithm for mutating quivers of 2-CY tilted algebras that have loops and 2-cycles, under certain specific conditions.
The universal cover of a representation finite algebra
P. Gabriel · 1981
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Covering spaces in representation-theory
K. Bongartz and P. Gabriel, · 1982
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Representation theory of artin algebras
M. Auslander, I. Reiten, S. Smalø · 1995
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Tilting in abelian categories and quasitilted algebras, Mem. Amer. Math. Soc
D. Happel, I. Reiten and S. O. Smalø · 1996
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Exzeptionelle Vektorbündel und Reflektionen an Kippgarben über Projektiven Gewichteten Kurven
Thomas Hübner · 1996
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Reflections and almost concealed canonical algebras
Thomas Hübner · 1997
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Cluster algebras. I. Foundations
Sergey Fomin and Andrei Zelevinsky · 2002
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On Triangulated orbit categories
B. Keller · 2005
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Locally finite triangulated categories
J. Xiao, Bin Zhu · 2005
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Cluster-tilted algebras of finite representation type
Aslak Bakke Buan, Robert J. Marsh, and Idun Reiten · 2006
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Tilting theory and cluster combinatorics
Aslak Bakke Buan, Robert Marsh, Markus Reineke, Idun Reiten, and Gordana Todorov · 2006
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Quivers with relations arising from clusters ( A n A_{n} case)
P. Caldero, F. Chapoton, and R. Schiffler · 2006
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Christof Geiß, Bernard Leclerc, and Jan Schröer · 2006
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On the structure of triangulated categories with finitely many indecomposables
Claire Amiot · 2007
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Cluster-tilted algebras
Aslak Bakke Buan, Robert J. Marsh, and Idun Reiten · 2007
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Quivers with potentials and their representations. I. Mutations
Harm Derksen, Jerzy Weyman, and Andrei Zelevinsky · 2008
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Mutation in triangulated categories and rigid Cohen-Macaulay modules
Osamu Iyama and Yuji Yoshino · 2008
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Acyclic Calabi-Yau categories, with an appendix by Michel Van den Bergh
B. Keller and I. Reiten · 2008
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The self-injective cluster-tilted algebras
Claus Michael Ringel · 2008
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A geometric model for cluster categories of type D n D_{n}
Ralf Schiffler · 2008
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Cluster structures for 2-Calabi-Yau categories and unipotent groups
Aslak B. Buan, Osamu Iyama, Idun Reiten, and Jeanne Scott · 2009
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Higher dimensional Auslander-Reiten theory on maximal orthogonal subcategories
Osamu Iyama · 2007
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Cluster tilting for one-dimensional hypersurface singularities
Igor Burban, Osamu Iyama, Bernhard Keller and Idun Reiten · 2008
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Cluster mutation via quiver representations
Aslak Bakke Buan, Robert J. Marsh, and Idun Reiten · 2008
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Mutation of cluster-tilting objects and potentials
Aslak B. Buan, Osamu Iyama, Idun Reiten, and David Smith
Cited in the paper.
Finding a cluster-tilting object for a representation finite cluster-tilted algebra
Marco A. Bertani-Økland, Steffen Opperman and Anette Wrålsen
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Graded mutation in cluster categories coming from hereditary categories with a tilting object
Marco Angel Bertani-Økland, Steffen Oppermann, and Anette Wrålsen
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Grothendieck group and generalized mutation rule for 2-Calabi-Yau triangulated categories
Yann Palu · 2009
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The mutation class of D n D_{n} quivers
Dagfinn Vatne · 2010
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