On structure of cluster algebras of geometric type Ⅰ：In view of sub-seeds and seed homomorphisms

作     者：Min Huang Fang Li Yichao Yang 

作者机构：Department of Mathematics Zhejiang University Hangzhou 310027 China Departement de Mathematiques Universite de Sherbrooke Sherbrooke J1K2R1 Canada 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2018年第61卷第5期

页      面：831-854页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by National Natural Science Foundation of China (Grant Nos. 11671350 and 11571173) 

主　　题：seed homomorphism mixing type sub seed rooted cluster morphism sub rooted cluster algebra rooted cluster quotient algebra 

摘      要：Our motivation is to build a systematic method in order to investigate the structure of cluster algebras of geometric type. The method is given through the notion of mixing-type sub-seeds, the theory of seed homomorphisms and the view-point of gluing of seeds. As an application, for(rooted) cluster algebras, we completely classify rooted cluster subalgebras and characterize rooted cluster quotient algebras in detail. Also,we build the relationship between the categorification of a rooted cluster algebra and that of its rooted cluster subalgebras. Note that cluster algebras of geometric type studied here are of the sign-skew-symmetric case.