Rogers dilogarithms of higher degree and generalized cluster algebras

TL;DR

This paper introduces a higher degree generalization of Rogers dilogarithms linked to generalized cluster algebras and proves identities associated with seed periods.

Contribution

It presents a novel higher degree Rogers dilogarithm and establishes identities related to seed periods in generalized cluster algebras.

Findings

Introduction of Rogers dilogarithms of higher degree

Proven identities for these dilogarithms associated with seed periods

Connection established between generalized cluster algebras and dilogarithm identities

Abstract

In connection with generalized cluster algebras we introduce a certain generalization of the celebrated Rogers dilogarithm, which we call the Rogers dilogarithms of higher degree. We show that there is an identity of these generalized Rogers dilogarithms associated with any period of seeds of a generalized cluster algebra.