Cluster algebras II: Finite type classification
摘要
This paper continues the study of cluster algebras initiated in math.RT/0104151. Its main result is the complete classification of the cluster algebras of finite type, i.e., those with finitely many clusters. This classification turns out to be identical to the Cartan-Killing classification of semisimple Lie algebras and finite root systems, which is intriguing since in most cases, the symmetry exhibited by the Cartan-Killing type of a cluster algebra is not at all apparent from its geometric origin. The combinatorial structure behind a cluster algebra of finite type is captured by its cluster complex. We identify this complex as the normal fan of a generalized associahedron introduced and studied in hep-th/0111053 and math.CO/0202004. Another essential combinatorial ingredient of our arguments is a new characterization of the Dynkin diagrams.
引用
@article{arxiv.math/0208229,
title = {Cluster algebras II: Finite type classification},
author = {Sergey Fomin and Andrei Zelevinsky},
journal= {arXiv preprint arXiv:math/0208229},
year = {2015}
}
备注
50 pages, 18 figures. Version 2: new introduction; final version, to appear in Invent. Math