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Quantum generalized cluster algebras and quantum dilogarithms of higher degrees. (English. Russian original) Zbl 1338.81241
Theor. Math. Phys. 185, No. 3, 1759-1768 (2015); translation from Teor. Mat. Fiz. 185, No. 3, 460-470 (2015).
Summary: We extend the notion of quantizing the coefficients of ordinary cluster algebras to the generalized cluster algebras of L. Chekhov and M. Shapiro [Int. Math. Res. Not. 2014, No. 10, 2746–2772 (2014; Zbl 1301.30042)]. 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.

##### MSC:
 81R50 Quantum groups and related algebraic methods applied to problems in quantum theory 17B37 Quantum groups (quantized enveloping algebras) and related deformations 11G55 Polylogarithms and relations with $$K$$-theory
##### Keywords:
cluster algebra; quantum dilogarithm
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##### References:
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