On structure of cluster algebras of geometric type I: In view of sub-seeds and seed homomorphisms
On structure of cluster algebras of geometric type I: In view of sub-seeds and seed homomorphisms
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DOI：
10.1007/s11425-016-9100-8
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发表时间：
2017-12
期刊：
影响因子：
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通讯作者：
Min-xin Huang;Fang Li;Yi-chao Yang
中科院分区：
文献类型：
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作者：
Min-xin Huang;Fang Li;Yi-chao Yang
我们的动机是建立一个系统的方法，以调查几何型的簇代数的结构。该方法是通过混合型子种子的概念、种子同态理论和种子胶合的观点给出的。作为应用，对于（有根）簇代数，我们对有根簇子代数进行了完全的分类，并对有根簇商代数进行了详细的刻画。同时，我们建立了一个根簇代数的范畴化与它的根簇子代数的范畴化之间的关系。注意，这里所研究的几何型的簇代数是符号斜对称的。
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.