English

Quantum generalized cluster algebras and quantum dilogarithms of higher degrees

Rings and Algebras 2017-03-01 v3 Quantum Algebra

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.

Keywords

Cite

@article{arxiv.1410.0584,
  title  = {Quantum generalized cluster algebras and quantum dilogarithms of higher degrees},
  author = {Tomoki Nakanishi},
  journal= {arXiv preprint arXiv:1410.0584},
  year   = {2017}
}

Comments

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