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On Structure of cluster algebras of geometric type I: In view of sub-seeds and seed homomorphisms
- Publication Year :
- 2015
-
Abstract
- 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.<br />Comment: 41 pages
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1509.01050
- Document Type :
- Working Paper