Cluster algebras
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[1] G. Moore,et al. Wall-crossing, Hitchin Systems, and the WKB Approximation , 2009, 0907.3987.
[2] R. Kedem. Q-systems as cluster algebras , 2007, 0712.2695.
[3] A. Vainshtein,et al. Cremmer–Gervais cluster structure on SLn , 2013, Proceedings of the National Academy of Sciences.
[4] Idun Reiten,et al. CLUSTER MUTATION VIA QUIVER REPRESENTATIONS , 2004 .
[5] Janice L. Malouf. An integer sequence from a rational recursion , 1992, Discret. Math..
[6] S. Fomin,et al. Cluster algebras II: Finite type classification , 2002, math/0208229.
[7] Sergey Fomin,et al. Polytopal Realizations of Generalized Associahedra , 2002, Canadian Mathematical Bulletin.
[8] G. Moore,et al. Four-Dimensional Wall-Crossing via Three-Dimensional Field Theory , 2008, 0807.4723.
[9] Tilting theory and cluster combinatorics , 2004, math/0402054.
[10] Cluster ensembles, quantization and the dilogarithm , 2003, math/0311245.
[11] C. Vafa,et al. T-branes and monodromy , 2010, 1010.5780.
[12] Y. Kodama,et al. KP solitons, total positivity, and cluster algebras , 2011, Proceedings of the National Academy of Sciences.
[13] A. Zelevinsky,et al. Greedy bases in rank 2 quantum cluster algebras , 2014, Proceedings of the National Academy of Sciences.
[14] C. Vafa,et al. BPS Quivers and Spectra of Complete N=2 Quantum Field Theories , 2011 .
[15] Moduli spaces of local systems and higher Teichmüller theory , 2003, math/0311149.
[16] S. Fomin,et al. Webs on surfaces, rings of invariants, and clusters , 2013, Proceedings of the National Academy of Sciences.
[17] Cluster Algebras and Poisson Geometry , 2002, math/0208033.
[18] N. Reshetikhin,et al. Representations of Yangians and multiplicities of occurrence of the irreducible components of the tensor product of representations of simple Lie algebras , 1990 .
[19] Sergey Fomin,et al. Generalized cluster complexes and Coxeter combinatorics , 2005, math/0505085.
[20] R. Kedem,et al. Q-systems as Cluster Algebras II: Cartan Matrix of Finite Type and the Polynomial Property , 2008, 0803.0362.
[21] A. Zelevinsky,et al. Quantum cluster algebras , 2004, math/0404446.
[22] R. Penner. The decorated Teichmüller space of punctured surfaces , 1987 .
[23] The F-triangle of the Generalised Cluster Complex , 2005, math/0509063.
[24] D. Thurston. Positive basis for surface skein algebras , 2013, Proceedings of the National Academy of Sciences.
[25] R. Stanley. Enumerative Combinatorics: Volume 1 , 2011 .
[26] B. Keller. The periodicity conjecture for pairs of Dynkin diagrams , 2010, 1001.1531.
[27] K. Goodearl,et al. Quantum cluster algebras and quantum nilpotent algebras , 2013, Proceedings of the National Academy of Sciences.
[28] M. Auslander,et al. Almost split sequences in subcategories , 1981 .
[29] George Lusztig,et al. Canonical bases arising from quantized enveloping algebras , 1990 .
[30] Sergey Fomin,et al. Cluster algebras III: Upper bounds and double Bruhat cells , 2003 .
[31] Cluster Ensembles, Quantization and the Dilogarithm II: The Intertwiner , 2007, math/0702398.
[32] J. Weyman,et al. Quivers with potentials and their representations I: Mutations , 2007, 0704.0649.
[33] J. Suzuki,et al. Periodicities of T-systems and Y-systems , 2008, Nagoya Mathematical Journal.
[34] L. Williams,et al. Positivity for cluster algebras from surfaces , 2009, 0906.0748.
[35] Rigid modules over preprojective algebras , 2005, math/0503324.
[36] A. A. Belavin,et al. Solutions of the classical Yang - Baxter equation for simple Lie algebras , 1982 .
[37] Li Li,et al. Greedy elements in rank 2 cluster algebras , 2012, 1208.2391.
[38] Sergey Fomin,et al. The Laurent Phenomenon , 2002, Adv. Appl. Math..
[39] Cluster algebras as Hall algebras of quiver representations , 2004, math/0410187.
[40] B. Leclerc,et al. Cluster algebras and quantum affine algebras , 2009, 0903.1452.
[41] Pierre-Guy Plamondon. Cluster algebras via cluster categories with infinite-dimensional morphism spaces , 2010, Compositio Mathematica.
[42] FROM DOMINOES TO HEXAGONS , 2004, math/0405482.
[43] H. Thomas,et al. Noncrossing partitions and representations of quivers , 2006, Compositio Mathematica.
[44] Gregg Musiker. A Graph Theoretic Expansion Formula for Cluster Algebras of Classical Type , 2007, 0710.3574.
[45] Claire Amiot. Cluster categories for algebras of global dimension 2 and quivers with potential , 2008, 0805.1035.
[46] various. Current Developments in Mathematics , 2008 .
[47] Anatol N. Kirillov. Dilogarithm identities , 1994 .
[48] J. Weyman,et al. Quivers with potentials and their representations II: Applications to cluster algebras , 2009, 0904.0676.
[49] A. Varchenko. The complex exponent of a singularity does not change along strataµ = const , 1982 .
[50] Ralf Schiffler. A Cluster Expansion Formula (An case) , 2008, Electron. J. Comb..
[52] On the properties of the exchange graph of a cluster algebra , 2007, math/0703151.
[53] C. Geiss,et al. Partial flag varieties and preprojective algebras , 2006, math/0609138.
[54] Ralf Schiffler,et al. On cluster algebras arising from unpunctured surfaces II , 2008, 0809.2593.
[55] Sergey Fomin,et al. Cluster algebras and triangulated surfaces. Part I: Cluster complexes , 2006 .
[56] Tomoki Nakanishi,et al. T-systems and Y-systems in integrable systems , 2010, 1010.1344.
[57] Alek Vainshtein,et al. Cluster algebras and Weil-Petersson forms , 2003 .
[58] B. Keller,et al. From triangulated categories to cluster algebras , 2005, math/0506018.
[59] Osamu Iyama,et al. Introduction to τ-tilting theory , 2013, Proceedings of the National Academy of Sciences.
[60] R. Penner,et al. On Quantizing Teichmüller and Thurston theories , 2004, math/0403247.
[61] A. Neitzke. Cluster-like coordinates in supersymmetric quantum field theory , 2014, Proceedings of the National Academy of Sciences.
[62] Lauren K. Williams,et al. Cluster algebras: an introduction , 2012, 1212.6263.
[63] R. Kashaev. Quantization of Teichmüller Spaces and the Quantum Dilogarithm , 1997, q-alg/9705021.
[64] J. Scott. Grassmannians and Cluster Algebras , 2003, math/0311148.
[65] S. Fomin,et al. Cluster algebras I: Foundations , 2001, math/0104151.
[66] C. Geiss,et al. Semicanonical bases and preprojective algebras , 2004, math/0402448.
[67] A. Hone. Laurent Polynomials and Superintegrable Maps , 2007, math/0702280.
[68] S. Fomin,et al. Y-systems and generalized associahedra , 2001, hep-th/0111053.
[69] Andrei Zelevinsky,et al. Semicanonical Basis Generators of the Cluster Algebra of Type A1(1) , 2006, Electronic Journal of Combinatorics.
[70] The quantum dilogarithm and representations of quantum cluster varieties , 2007, math/0702397.
[71] Thermodynamic Bethe Ansatz and Dilogarithm Identities I , 1995, hep-th/9506215.
[72] S. D. Chatterji. Proceedings of the International Congress of Mathematicians , 1995 .
[73] C. Vafa,et al. BPS Quivers and Spectra of Complete $${\mathcal{N} = 2}$$N=2 Quantum Field Theories , 2011, 1109.4941.
[74] B. Keller,et al. Linear independence of cluster monomials for skew-symmetric cluster algebras , 2012, Compositio Mathematica.
[75] C. Vafa,et al. Classification of Complete N = 2 Supersymmetric Theories in 4 Dimensions , 2011, 1103.5832.
[76] Andrei Zelevinsky,et al. Generalized associahedra via quiver representations , 2002, math/0205152.
[77] Cluster algebras: Notes for the CDM-03 conference , 2003, math/0311493.