Quantum dilogarithm identities and cyclic quivers

Abstract

We study quantum dilogarithm identities for cyclic quivers following Reineke's idea via Ringel-Hall algebra approach. For any given discrete stability function for the cyclic quiver $Δ_n$ with $n$ vertices, we obtain certain cyclic quantum dilogarithm identities of order $n$ in the sense of Bytsko and Volkov.

11 pages