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We extend the construction of canonical bases for cluster algebras from unpunctured surfaces to the case where the number of marked points is one, and we show that the cluster algebra is equal to the upper cluster algebra in this case.
R. Schiffler, On cluster algebras arising from unpunctured surfaces II, Adv. Math. 223
1923
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G. Lusztig, Canonical bases arising from quantized enveloping algebras. J. Amer. Math. Soc 3
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G. Lusztig, Introduction to quantum groups , Progress in Mathematics 110, Birkhauser, 1993
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S. Fomin and A. Zelevinsky, Cluster algebras I: Foundations, J. Amer. Math. Soc. 15
2002
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S. Fomin and A. Zelevinsky, Cluster algebras II. Finite type classification. Invent. Math. 154
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A. Berenstein, S. Fomin and A. Zelevinsky, Cluster algebras. III. Upper bounds and double Bruhat cells. Duke Math. J. 126
2005
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M. Gekhtman, M. Shapiro and A. Vainshtein, Cluster algebras and Weil-Petersson forms, Duke Math. J. 127
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V. Fock and A. Goncharov, Moduli spaces of local systems and higher Teichmüller theory. Publ. Math. Inst. Hautes Études Sci
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S. Fomin and A. Zelevinsky, Cluster algebras IV: Coefficients, Compositio Mathematica 143
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S. Fomin, M. Shapiro and D. Thurston, Cluster algebras and triangulated surfaces. Part I: Cluster complexes, Acta Math. 201
2008
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S. Fomin and D. Thurston, Cluster algebras and triangulated surfaces. Part II: Lambda Lengths, preprint (2008), http://www.math.lsa.umich.edu/ ∼ \sim fomin/Papers/cats2.ps
2008
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R. Schiffler, A cluster expansion formula ( A n A_{n} case), Electron. J. Combin. 15 (2008), #R64 1
2008
Cited alongside, same era.
V. Fock and A. Goncharov, Cluster ensembles, quantization and the dilogarithm, Ann. Sci. Ec. Norm. Super. (4) 42, (2009), no. 6, 865–930
2009
Cited alongside, same era.
R. Schiffler and H. Thomas, On cluster algebras arising from unpunctured surfaces, Int. Math. Res. Not. no. 17, (2009), 3160–3189
2009
Cited alongside, same era.
A. Felikson, M. Shapiro and P. Tumarkin, Cluster algebras of finite mutation type via unfoldings, Int. Math. Res. Not
2012
Later among the works it cites.
A. Felikson, M. Shapiro and P. Tumarkin, Cluster algebras and triangulated orbifolds, Adv. Math
2012
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M. Alim, S. Cecotti, C. Cordova, S. Espahbodi, A. Rastogi, and C. Vafa, BPS Quivers and Spectra of Complete N=2 Quantum Field Theories, Comm. Math. Phys
2013
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T. Brüstle, G. Dupont and M. Pérotin, On maximal green sequences, IMRN (2013)
2013
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I. Canakci and R. Schiffler, Snake graph calculus and cluster algebras from surfaces, J. Algebra
2013
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G. Muller, Locally acyclic cluster algebras, Adv. Math. 233
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G. Musiker and R. Schiffler, Cluster expansion formulas and perfect matchings, J. Algebraic Combin. 32
2010
Cited alongside, same era.
B. Keller, On cluster theory and quantum dilogarithm identities, Representations of algebras and related topics, 85–116, EMS Ser. Congr. Rep., Eur. Math. Soc. , Zrich, 2011
2011
Cited alongside, same era.
G. Musiker, R. Schiffler and L. Williams, Positivity for cluster algebras from surfaces, Adv. Math. 227
2011
Cited alongside, same era.
A. Felikson, M. Shapiro and P. Tumarkin, Skew-symmetric cluster algebras of finite mutation type, J. Eur. Math. Soc
2012
Cited alongside, same era.
Cited in the paper.
I. Canakci and R. Schiffler, Snake graph calculus and cluster algebras from surfaces III, in preparation
Cited in the paper.
Cited in the paper.
2013
Later among the works it cites.
G. Musiker, R. Schiffler and L. Williams, Bases for cluster algebras from surfaces, Compos. Math. 149
2013
Later among the works it cites.
G. Musiker and L. Williams, Matrix formulae and skein relations for cluster algebras from surfaces, Int. Math. Res. Notices,
2013
Later among the works it cites.
D. Thurston, A positive basis for surface skein algebras, PNAS
2014
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