Cluster ensembles, quantization and the dilogarithm

Annales Scientifiques de l'Ecole Normale Superieure

Volumn 42, Issue 6, 2009, Pages 865-930

  Fock, Vladimir V ^a   Goncharov, Alexander B ^b  

^a UNIVERSITÉ DE STRASBOURG   (France)

^b BROWN UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77952074059     PISSN: 00129593     EISSN: None     Source Type: Journal    
DOI: 10.24033/asens.2112     Document Type: Article

References (26)

1. A. BERENSTEIN, S. FOMIN, A. ZELEVINSKY, Cluster algebras. III. Upper bounds and double Bruhat cells, Duke Math. J. 126 (2005), 1-52.
2. A. BERENSTEIN, A. ZELEVINSKY, Quantum cluster algebras, Adv. Math. 195 (2005), 405-455. (Pubitemid 40664842)
3. J. W. CANNON, W. J. FLOYD, W. R. PARRY, Introductory notes on Richard Thompson's groups, Enseign. Math. 42 (1996), 215-256. (Pubitemid 127007156)
4. F CHAPOTON, S. FOMIN, A. ZELEVINSKY, Polytopal realizations of generalized associahedra, Canad. Math. Bull. 45 (2002), 537-566.
5. V. V. FOCK, A. B. GONCHAROV, Cluster X-varieties, amalgamation, and Poisson-Lie groups, in Algebraic geometry and number theory, Progr. Math. 253, Birkhäuser, 2006, 27-68.
6. V. V. FOCK, A. B. GONCHAROV, Moduli spaces of local systems and higher Teichmüller theory, Publ. Math. Inst. Hautes Études Sci. 103(2006), 1-211.
7. V. V. FOCK, A. B. GONCHAROV, Dual Teichmüller and lamination spaces, in Handbook of Teichmüller theory. Vol. I, IRMA Lect. Math. Theor. Phys. 11, Eur. Math. Soc, Zürich, 2007, 647-684.
8. V. V. FOCK, A. B. GONCHAROV, Cluster ensembles, quantization and the dilogarithm II: The intertwiner, Progress in Math. 269 (2009), 513-524.
9. V. V. FOCK, A. B. GONCHAROV, The quantum dilogarithm and representations of quantum cluster varieties, Invent. Math. 175 (2009), 223-286.
10. V. V. FOCK, A. B. GONCHAROV, Completions of cluster varieties, to appear.
11. V. V. FOK, L. O. CHEKHOV, Quantum Teichmüller spaces, Teoret. Mat. Fiz. 120 (1999), 511-528.
12. S. FOMIN, A. ZELEVINSKY, Cluster algebras. I. Foundations, J. Amer Math. Soc. 15 (2002), 497-529 (electronic).
13. S. FOMIN, A. ZELEVINSKY, The Laurent phenomenon, Adv. in Appl. Math. 28 (2002), 119-144.
14. S. FOMIN, A. ZELEVINSKY, Cluster algebras. II. Finite type classification, Invent. Math. 154 (2003), 63-121. (Pubitemid 37223721)
15. S. FOMIN, A. ZELEVINSKY, Y-systems and generalized associahedra, Ann. of Math. 158 (2003), 977-1018. (Pubitemid 38285153)
16. M. GEKHTMAN, M. SHAPIRO, A. VAINSHTEIN, Cluster algebras and Poisson geometry, Mosc. Math. J. 3 (2003), 899-934.
17. M. GEKHTMAN, M. SHAPIRO, A. VAINSHTEIN, Cluster algebras and Weil-Petersson forms, Duke Math. J. 127 (2005), 291-311. (Pubitemid 40622648)
18. A. B. GONCHAROV, Explicit construction of characteristic classes, in I. M. Gel'fand Seminar, Adv. Soviet Math. 16, Amer. Math. Soc, 1993, 169-210.
19. A. B. GONCHAROV, Geometry of configurations, polylogarithms, and motivic cohomology, Adv. Math. 114 (1995), 197-318.
20. cyc, in Geometry anddynamics of groups and spaces, Progr. Math. 265, Birkhäuser, 2008, 415-428.
21. M. IMBERT, Sur l'isomorphisme du groupe de Richard Thompson avec le groupe de Ptolémée, in Geometric Galois actions, 2, London Math. Soc. Lecture Note Ser. 243, Cambridge Univ. Press, 1997, 313-324.
22. R. M. KASHAEV, Quantization of Teichmüller spaces and the quantum dilogarithm, Lett. Math. Phys. 43(1998), 105-115. (Pubitemid 128503751)
23. J. MILNOR, Introduction to algebraic K-theory, Annals of Math. Studies 72, Princeton Univ. Press, 1971.
24. R. C. PENNER, The decorated Teichmüller space of punctured surfaces, Comm. Math. Phys. 113 (1987), 299-339.
25. P. SHERMAN, A. ZELEVINSKY, Positivity and canonical bases in rank 2 cluster algebras of finite and affine types, Mosc. Math. J. 4 (2004), 947-974.
26. 3 of a field and the Bloch group, Proc. Steklov Inst. Math. N4 (1991), 217-239.