Geodesic
Quantum generalized cluster algebras and quantum dilogarithms of higher degrees
Teoretičeskaâ i matematičeskaâ fizika, Tome 185 (2015) no. 3, pp. 460-470

Voir la notice de l'article provenant de la source Math-Net.Ru

We extend the notion of quantizing the coefficients of ordinary cluster algebras to the generalized cluster algebras of 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: cluster algebra, quantum dilogarithm. 
@article{TMF_2015_185_3_a4,
     author = {T. Nakanishi},
     title = {Quantum generalized cluster algebras and quantum dilogarithms of higher degrees},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {460--470},
     publisher = {mathdoc},
     volume = {185},
     number = {3},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2015_185_3_a4/}
}
TY  - JOUR
AU  - T. Nakanishi
TI  - Quantum generalized cluster algebras and quantum dilogarithms of higher degrees
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2015
SP  - 460
EP  - 470
VL  - 185
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_2015_185_3_a4/
LA  - ru
ID  - TMF_2015_185_3_a4
ER  - 
%0 Journal Article
%A T. Nakanishi
%T Quantum generalized cluster algebras and quantum dilogarithms of higher degrees
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2015
%P 460-470
%V 185
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_2015_185_3_a4/
%G ru
%F TMF_2015_185_3_a4
T. Nakanishi. Quantum generalized cluster algebras and quantum dilogarithms of higher degrees. Teoretičeskaâ i matematičeskaâ fizika, Tome 185 (2015) no. 3, pp. 460-470. http://geodesic.mathdoc.fr/item/TMF_2015_185_3_a4/