an:07042766
Zbl 1408.16008
Bai, Liqian; Chen, Xueqing; Ding, Ming; Xu, Fan
A quantum analog of generalized cluster algebras
EN
Algebr. Represent. Theory 21, No. 6, 1203-1217 (2018).
00431384
2018
j
16G20 17B67 17B35 18E30
generalized cluster algebra; generalized quantum cluster algebra; Laurent phenomenon; standard monomial
Summary: 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 [\textit{A. Berenstein} and \textit{A. Zelevinsky}, Adv. Math. 195, No. 2, 405--455 (2005; Zbl 1124.20028)]. In the case of rank two, we extend some structural results from the classical theory of generalized cluster algebras obtained in [\textit{L. Chekhov} and \textit{M. Shapiro}, Int. Math. Res. Not. 2014, No. 10, 2746--2772 (2014; Zbl 1301.30042)] and [\textit{D. Rupel}, ``Greedy bases in rank 2 generalized cluster algebras'', Preprint, \url{arXiv:1309.2567}] to the quantum case.
Zbl 1124.20028; Zbl 1301.30042