Bazhanov, V. V.; Reshetikhin, N. Yu. Remarks on the quantum dilogarithm. (English) Zbl 0876.17035 J. Phys. A, Math. Gen. 28, No. 8, 2217-2226 (1995). Summary: A quantum analogue of the dilogarithm function has been introduced recently by L. D. Faddeev and R. M. Kashaev [Mod. Phys. Lett. A 9, 427-434 (1994; Zbl 0866.17010)] in such a way that a certain identity in the Weyl algebra \(\overline W_q\) plays the role of the five-term dilogarithm identity. We study this identity in the limit when \(q\) approaches a root of unity and show that it then reduces to the ‘restricted star-triangle relation’ which has been used previously by V. V. Bazhanov and R. J. Baxter [J. Stat. Phys. 71, 839-864 (1993; Zbl 0876.17031)] as a local integrability condition of a class of three-dimensional solvable lattice models. Cited in 9 Documents MSC: 17B81 Applications of Lie (super)algebras to physics, etc. 33B99 Elementary classical functions 81R50 Quantum groups and related algebraic methods applied to problems in quantum theory 82B23 Exactly solvable models; Bethe ansatz 17B37 Quantum groups (quantized enveloping algebras) and related deformations Keywords:quantum dilogarithm; restricted star-triangle relation; dilogarithm identity; solvable lattice models Citations:Zbl 0876.17031; Zbl 0866.17010 PDFBibTeX XMLCite \textit{V. V. Bazhanov} and \textit{N. Yu. Reshetikhin}, J. Phys. A, Math. Gen. 28, No. 8, 2217--2226 (1995; Zbl 0876.17035) Full Text: DOI