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 homomorph...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.展开更多
Based on a graph-theoretic analysis,we determine all the irreducible reflection subgroups of the imprimitive complex reflection groups G(m,p,n),and describe the irreducible subsystems of all possible types in the root...Based on a graph-theoretic analysis,we determine all the irreducible reflection subgroups of the imprimitive complex reflection groups G(m,p,n),and describe the irreducible subsystems of all possible types in the root system R(m,p,n) of G(m,p,n).展开更多
基金supported by National Natural Science Foundation of China (Grant Nos. 11671350 and 11571173)
文摘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.
基金supported by National Natural Science Foundation of China(Grant Nos.10631010,10971138)the General Research Project of Shanghai Normal University (Grant No.SK200702)+2 种基金the Science Foundation of University Doctoral Project of China (Grant No.20060269011)Program for Changjiang Scholars and Innovative Research Team in University (Grant No.41192803)Shanghai Leading Academic Discipline Project (Grant No.B407)
文摘Based on a graph-theoretic analysis,we determine all the irreducible reflection subgroups of the imprimitive complex reflection groups G(m,p,n),and describe the irreducible subsystems of all possible types in the root system R(m,p,n) of G(m,p,n).
