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Yang-Baxterization of quantum dilogarithm. (Russian. English summary) Zbl 0893.17014
Faddeev, L. D. (ed.) et al., Problems in quantum field theory and statistical physics. 13. Work collection. Dedicated to the memory of V. N. Popov. Sankt-Peterburg: Nauka. Zap. Nauchn. Semin. POMI. 224, 146-154 (1995).
Summary: A new solution of the Yang-Baxter relation with spectral parameter is found. The obtained $$R$$-matrix $$R(x)$$ is an operator in $${\mathcal H}\otimes{\mathcal H}$$, where $${\mathcal H}= L_2(\mathbb{R})$$. This $$R$$-matrix is required for the justification of the solution of the sine-Gordon model on discrete space-time, constructed by the authors recently [L. D. Faddeev and A. Yu. Volkov, Lett. Math. Phys. 32, 125-135 (1994; Zbl 0807.35124)].
For the entire collection see [Zbl 0868.00027].

##### MSC:
 17B37 Quantum groups (quantized enveloping algebras) and related deformations 35Q53 KdV equations (Korteweg-de Vries equations) 81R50 Quantum groups and related algebraic methods applied to problems in quantum theory 33B99 Elementary classical functions
##### Keywords:
Yang-Baxter relation; $$R$$-matrix; sine-Gordon model