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Inspired by recent work of Geiss-Leclerc-Schroer, we use Hom-finite cluster categories to give a good candidate set for a basis of (upper) cluster algebras with coefficients arising from quivers.
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Grégoire Dupont, Generic cluster characters , International Mathematics Research Notices IMRN (2011), doi: 10.1093/imrn/rnr024
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by same author, Generic variables in acyclic cluster algebras , J. Pure Appl. Algebra 215
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by same author, Calabi-Yau triangulated categories , Trends in representation theory of algebras and related topics, EMS Ser. Congr. Rep., Eur. Math. Soc., Zürich, 2008, pp. 467–489
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by same author, Cluster characters for 2-Calabi-Yau triangulated categories , Ann. Inst. Fourier (Grenoble) 58
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Claire Amiot, Cluster categories for algebras of global dimension 2 and quivers with potential , Ann. Inst. Fourier (Grenoble) 59
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by same author, Cluster ensembles, quantization and the dilogarithm , Ann. Sci. Éc. Norm. Supér. (4) 42
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Kiyoshi Igusa, Kent Orr, Gordana Todorov and Jerzy Weyman, Cluster complexes via semi-invariants , Compos. Math. 145
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by same author, Quivers with potentials associated to triangulated surfaces , Proc. Lond. Math. Soc. (3) 98
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by same author, Quivers with potentials and their representations II: applications to cluster algebras , J. Amer. Math. Soc. 23
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Christof Geiss, Bernard Leclerc, and Jan Schröer, Kac–Moody groups and cluster algebras , Advances in Mathematics 228
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Bernhard Keller, Deformed Calabi–Yau completions , to appear in Crelle’s Journal, doi: 10.1515/CRELLE.2011.031
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Bernhard Keller and Dong Yang, Derived equivalences from mutations of quivers with potential , Advances in Mathematics 226
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Hiraku Nakajima, Quiver varieties and cluster algebras , Kyoto J. Math. 51
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by same author, Cluster characters for cluster categories with infinite-dimensional morphism spaces , Advances in Mathematics 227
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by same author, Generic bases for cluster algebras and the Chamber Ansatz , J. Amer. Math. Soc. 25
2012
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