论文标题
从表面和扩展的仿生Weyl组的群集代数
Cluster algebras from surfaces and extended affine Weyl groups
论文作者
论文摘要
我们使用阳性半明确二次形式表征至少3个等级的突变 - 芬特群集代数。特别是，我们与每个不牢固的边界表面相关联，一个正半决的二次空间$ v $，并且每个三角剖分都是$ v $的基础，以使群集的任何突变（即三角剖分的翻转）通过部分反射将相应的基础转化为相应的基础。此外，每个三角剖分都会产生$ a $ a $的延长仿型Weyl群，这是不变的。该结构还扩展到了$ e $ $ e $的特殊偏斜突变 - 限制群集代数。
We characterize mutation-finite cluster algebras of rank at least 3 using positive semi-definite quadratic forms. In particular, we associate with every unpunctured bordered surface a positive semi-definite quadratic space $V$, and with every triangulation a basis in $V$, such that any mutation of a cluster (i.e., a flip of a triangulation) transforms the corresponding bases into each other by partial reflections. Furthermore, every triangulation gives rise to an extended affine Weyl group of type $A$, which is invariant under flips. The construction is also extended to exceptional skew-symmetric mutation-finite cluster algebras of types $E$.
