Rogers dilogarithms of higher degree and generalized cluster algebras

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.

32 pages; v2:minor changes; v3:Prop. 4.3 added, the condition (A.11) removed; v4: Defs. 4.2 & A.4 changed + minor changes

References in corpus (3)

• The quantum dilogarithm and representations quantum cluster varieties
• Structure of seeds in generalized cluster algebras
• Quantum generalized cluster algebras and quantum dilogarithms of higher degrees

Cited by in corpus (1)

• On webs, polylogarithms and cluster algebras