有限型簇代数与正对称化矩阵
组合数学
2019-03-05 v5 表示论
摘要
本文的动机来自簇代数与 Kac-Moody 代数之间的类比：两种理论都通过熟知的 Cartan-Killing 类型对有限型对象进行相同的分类。然而，这两种分类背后的组合结构是不同的：粗略地说，Kac-Moody 代数与（可对称化的）Cartan 矩阵相关联，而簇代数对应于斜对称化矩阵。我们研究这两类矩阵之间的相互作用，特别地，建立一个新准则以判定给定的斜对称化矩阵是否产生有限型簇代数。
引用
@article{arxiv.math/0411341,
title = {Cluster algebras of finite type and positive symmetrizable matrices},
author = {Michael Barot and Christof Geiss and Andrei Zelevinsky},
journal= {arXiv preprint arXiv:math/0411341},
year = {2019}
}
备注
20 pages. In version 3, some new material is added in the end of section 2, discussing the classification and characterizations of positive quasi-Cartan matrices. In final version 4, Proposition 2.9 is corrected and its proof expanded. To appear in J. London Math. Soc. In version 5 only typos in the arXiv data fixed