A Quantum Analog of Generalized Cluster Algebras

作者：Bai, Liqian; Chen, Xueqing; Ding, Ming^*; Xu, Fan

来源：Algebras and Representation Theory, 2018, 21(6): 1203-1217.

DOI：10.1007/s10468-017-9743-7

• Generalized cluster algebra
• Generalized quantum cluster algebra
• Laurent phenomenon
• Standard monomial

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.

• 出版日期2018-12
• 单位西北工业大学; 清华大学; 南开大学