A Quantum Analog of Generalized Cluster Algebras

被引：3

作者：

Bai, Liqian ^{[1
]}

Chen, Xueqing ^{[2
]}

Ding, Ming ^{[3
,4
]}

Xu, Fan ^{[5
]}

机构：

[1] Northwestern Polytech Univ, Dept Appl Math, Xian 710072, Shaanxi, Peoples R China

[2] Univ Wisconsin, Dept Math, 800 W Main St, Whitewater, WI 53190 USA

[3] Nankai Univ, Sch Math Sci, Tianjin, Peoples R China

[4] Nankai Univ, LPMC, Tianjin, Peoples R China

[5] Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China

来源：

ALGEBRAS AND REPRESENTATION THEORY | 2018年 / 21卷 / 06期

基金：

高等学校博士学科点专项科研基金; 中国国家自然科学基金;

关键词：

Generalized cluster algebra; Generalized quantum cluster algebra; Laurent phenomenon; Standard monomial; DILOGARITHM;

D O I：

10.1007/s10468-017-9743-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We define a quantum analog of a class of generalized cluster algebras which can be viewed as a generalization of quantum cluster algebras defined in Berenstein and Zelevinsky (Adv. Math. 195(2), 405-455 2005). In the case of rank two, we extend some structural results from the classical theory of generalized cluster algebras obtained in Chekhov and Shapiro (Int. Math. Res. Notices 10, 2746-2772 2014) and Rupel (2013) to the quantum case.

引用

页码：1203 / 1217

页数：15