Cluster characters for cyclic quivers

作     者：Ming DING Fan XU 

作者机构：School of Mathematical Sciences Nankai University Tianjin 300071 China Department of Mathematical Sciences Tsinghua University Beijing 100084 China 

出 版 物：《Frontiers of Mathematics in China》 (中国高等学校学术文摘·数学（英文）)

年 卷 期：2012年第7卷第4期

页      面：679-693页

核心收录：

学科分类：1305[艺术学-设计学（可授艺术学、工学学位）] 080904[工学-电磁场与微波技术] 0810[工学-信息与通信工程] 13[艺术学] 0809[工学-电子科学与技术（可授工学、理学学位）] 08[工学] 080402[工学-测试计量技术及仪器] 0804[工学-仪器科学与技术] 081001[工学-通信与信息系统] 

基　　金：Supported by the Fundamental Research Funds for the Central Universities Supported by Alexander von Humboldt Stiftung Supported by the Ph. D. Programs Foundation of Ministry of Education of China 

主　　题：Cyclic quiver cluster algebra Z-basis 

摘      要：We define an analogue of the Caldero-Chapoton map for the cluster category of finite-dimensional nilpotent representations over a cyclic quiver. We prove that it is a cluster character and satisfies some inductive formulas for the multiplication between the generalized cluster variables （the images of objects of the cluster category under this map）. Moreover, we construct a Z-basis for the algebra generated by all generalized cluster variables.