Remarks on the quantum dilogarithm

Abstract

A quantum analogue of the dilogarithm function has been introduced by Faddeev and Kashaev (1994) in such a way that a certain identity in the Weyl algebra 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 Bazhanov and Baxter (1992) as a local integrability condition of a class of three-dimensional solvable lattice models.