Rogers dilogarithms of higher degree and generalized cluster algebras

This is the authors' abstract. We don't add key points for this paper.

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.