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This is a brief survey on the recently developing tropicalization method in cluster algebras and its applications to the periodicities of Y-systems and the associated dilogarithm identities.
1954
Earlier work this paper cites.
1960
Earlier work this paper cites.
L. Lewin, Polylogarithms and associated functions , North-Holland, Amsterdam, 1981
1981
Earlier work this paper cites.
A. N. Kirillov, Identities for the Rogers dilogarithm function connected with simple Lie algebras , J. Sov. Math. 47
1989
Earlier work this paper cites.
V. V. Bazhanov and N. Yu. Reshetikhin, Restricted solid-on-solid models connected with simply laced algebras and conformal field theory , J. Phys. A: Math. Gen. 23
1990
Earlier work this paper cites.
A. N. Kirillov and N. Yu. Reshetikhin, Representations of Yangians and multiplicities of the inclusion of the irreducible components of the tensor product of representations of simple Lie algebras, , J. Sov. Math. 52
1990
Earlier work this paper cites.
Al. B. Zamolodchikov, On the thermodynamic Bethe ansatz equations for reflectionless ADE scattering theories , Phys. Lett. B253
1991
Earlier work this paper cites.
L. D. Faddeev and A. Yu. Volkov, Abelian current algebra and the Virasoro algebra on the lattice , Phys. Lett. 315
1993
Earlier work this paper cites.
A. Kuniba, Thermodynamics of the U q ( X r ( 1 ) ) U_{q}(X^{(1)}_{r}) Bethe ansatz system with q q a root of unity , Nucl. Phys. B389
1993
Earlier work this paper cites.
R. Ravanini, R. Tateo, and A. Valleriani, Dynkin TBA’s , Int. J. Mod. Phys. A8
1993
Earlier work this paper cites.
A. Kuniba, T. Nakanishi, and J. Suzuki, Functional relations in solvable lattice models: I. Functional relations and representation theory , Int. J. Mod. Phys. A9
1994
Earlier work this paper cites.
E. Frenkel and A. Szenes, Thermodynamic Bethe ansatz and dilogarithm identities. I , Math. Res. Lett. 2
1995
Earlier work this paper cites.
F. Gliozzi and R. Tateo, ADE functional dilogarithm identities and integrable models , Phys. Lett. B348
1995
Earlier work this paper cites.
by same author, Dilogarithm identities , Prog. Theor. Phys. Suppl. 118
1995
Earlier work this paper cites.
F. Gliozzi and R. Tateo, Thermodynamic Bethe ansatz and three-fold triangulations , Int. J. Mod. Phys. A11
1996
Earlier work this paper cites.
S. Fomin and A. Zelevinsky, Cluster algebras I. Foundations , J. Amer. Math. Soc. 15
2002
Earlier work this paper cites.
S. Fomin and A. Zelevinsky, Cluster algebras II. Finite type classification , Invent. Math. 154
2003
Earlier work this paper cites.
by same author, Y-systems and generalized associahedra , Ann. of Math. 158
2003
Earlier work this paper cites.
A. Berenstein, S. Fomin, and A. Zelevinsky, Cluster algebras III: upper bounds and double Bruhat cells , Duke Math. J. 126
2005
Cited alongside, same era.
A. Berenstein and A. Zelevinsky, Quantum cluster algebras , Adv. in Math. 195
2005
Cited alongside, same era.
F. Chapoton, Functional identities for the Rogers dilogarithm associated to cluster Y-systems , Bull. London Math. Soc. 37
2005
Cited alongside, same era.
A. Buan, R. Marsh, M. Reineke, I. Reiten, and G. Todorov, Tilting theory and cluster combinatorics , Adv. in Math. 204
2006
Cited alongside, same era.
P. Caldero and F. Chapoton, Cluster algebras as Hall algebras of quiver representations , Comment. Math. Helv. 81
2006
Cited alongside, same era.
2010
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2010
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2010
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2010
Later among the works it cites.
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2007
Cited alongside, same era.
A. Y. Volkov, On the periodicity conjecture for Y-systems , Commun. Math. Phys. 276
2007
Cited alongside, same era.
D. Zagier, The dilogarithm function , Frontiers in Number Theory, Physics, and Geometry II, Springer, Berlin, Heidelberg, 2007, pp. 3–65
2007
Cited alongside, same era.
2008
Cited alongside, same era.
Y. Palu, Cluster characters for triangulated 2-Calabi-Yau triangulated categories , Annales de l’institut Fourier 58
2008
Cited alongside, same era.
2009
Cited alongside, same era.
V. V. Fock and A. B. Goncharov, Cluster ensembles, quantization and the dilogarithm , Annales Sci. de l’École Norm. Sup. 42
2009
Cited alongside, same era.
2010
Later among the works it cites.
K. Nagao, Donaldson-Thomas theory and cluster algebras , 2010, arXiv:1002.4884 [math.AG]
2010
Later among the works it cites.
2010
Later among the works it cites.
F. Qin, Quantum cluster variables via Serre polynomials , 2010, arXiv:1004.4171 [math.QA]
2010
Later among the works it cites.
2011
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R. M. Kashaev and T. Nakanishi, Classical and quantum dilogarithm identities , SIGMA 7
2011
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2011
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K. Nagao, Quantumd dilogarithm identities , RIMS Kôkyûroku Bessatsu B28
2011
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K. Nagao, Wall-crossing of the motivic Donaldson-thomas invariants , 2011, arXiv:1103.2922 [math.AG]
2011
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T. Nakanishi, Dilogarithm identities for conformal field theories and cluster algebras: Simply laced case , Nagoya Math. J. 202
2011
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2011
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2011
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