Quantum dilogarithm identities and cyclic quivers

TL;DR

This paper explores quantum dilogarithm identities associated with cyclic quivers, employing Ringel-Hall algebra techniques to derive new cyclic identities based on stability functions.

Contribution

It introduces cyclic quantum dilogarithm identities of order n for cyclic quivers using a Ringel-Hall algebra approach, extending prior work on quantum identities.

Findings

Derived cyclic quantum dilogarithm identities for cyclic quivers.

Established a framework connecting stability functions with quantum identities.

Extended the understanding of quantum dilogarithm relations in the context of 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 $\Delta_n$ with $n$ vertices, we obtain certain cyclic quantum dilogarithm identities of order $n$ in the sense of Bytsko and Volkov.