Quantum generalized cluster algebras and quantum dilogarithms of higher degrees

Abstract

We extend the notion of the quantization of the coefficients of the ordinary cluster algebras to the generalized cluster algebras by Chekhov and Shapiro. In parallel to the ordinary case, it is tightly integrated with certain generalizations of the ordinary quantum dilogarithm, which we call the quantum dilogarithms of higher degrees. As an application, we derive the identities of these generalized quantum dilogarithms associated with any period of quantum Y-seeds.

10 pages; v2. reference corrected, to appear in Theor. Math. Phys; v3. typo in (4.5) corrected

References in corpus (3)

• The quantum dilogarithm and representations quantum cluster varieties
• Exact WKB analysis and cluster algebras II: Simple poles, orbifold points, and generalized cluster algebras
• Structure of seeds in generalized cluster algebras

Cited by in corpus (1)

• Rogers dilogarithms of higher degree and generalized cluster algebras