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The new form of pentagon equations suggested by Volkov for the $ q $-exponential on the basis of formal series is derived within the Hilbert space framework for the modular version of the quantum dilogarithm.
Marcel Paul Schützenberger, Une interprétation de certaines solutions de l’équation fonctionnelle: F ( x + y ) = F ( x ) F ( y ) F(x+y)=F(x)F(y) , C. R. Acad. Sci. Paris 236
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L. Faddeev, A.Yu. Volkov, Theor. Math. Phys. 92 (1992) 207, preprint HU-TFT-93-30
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L. D. Faddeev and R. M. Kashaev, “Quantum Dilogarithm,” Mod. Phys. Lett. A 9
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L. Faddeev, A.Yu. Volkov, “Hirota equation as an example of integrable symplectic map,” Lett. Math. Phys. 32
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L. D. Faddeev, “Discrete Heisenberg-Weyl group and modular group,” Lett. Math. Phys. 34
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L. D. Faddeev, “Modular double of quantum group,” Math. Phys. Stud. 21
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R. Kashaev and T. Nakanishi, Classical and quantum dilogarithm identities, arXiv:1104.4630 [math.QA]
Cited in the paper.
Barnes E.W.: The genesis of the double gamma function . Proc. London Math. Soc. 31 (1899) 358-381
L. D. Faddeev, R. M. Kashaev and A. Y. Volkov, “Strongly coupled quantum discrete Liouville theory. 1. Algebraic approach and duality,” Commun. Math. Phys. 219
2001
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B. Ponsot and J. Teschner, “Clebsch-Gordan and Racah-Wigner coefficients for a continuous series of representations of U q ( s l ( 2 , R ) ) U_{q}(sl(2,R)) ”, Comm. Math. Phys. 224
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A. Yu. Volkov, “Noncommutative Hypergeometry”, Commun. Math. Phys. 258
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2011
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Cited in the paper.
R. M. Kashaev, “Liouville central charge in quantum Teichmuller theory,” arXiv:hep-th/9811203
Cited in the paper.
Chekhov L., Fock V. Quantum Teichmüller spaces. ArXive, math.QA/9908165
Cited in the paper.