Quantum dilogarithm identities arising from the product formula for the universal R-matrix of quantum affine algebras (Q6143267)

The paper under review gives an alternative algebraic proof of the four quantum dilogarithm identities which are originally due to \textit{T. Dimofte} et al. [Lett. Math. Phys. 95, No. 1, 1--25 (2011; Zbl 1205.81113)]. The new approach uses the formula for the universal R-matrix of the quantum affine algebra which is due to Ito. This gives various product presentations of the universal R-matrix by choosing various convex orders on an affine root system. This leads to a number of quantum dilogarithm identities, where the ones mentioned above correspond to convex orders of multiple row type.