标题： Ind-簇代数和无限 Grassmannian 显示英文标题

标题： Ind-cluster algebras and infinite Grassmannians

摘要： 簇代数的一个典型例子是有限Grassmannian的坐标环：利用Plücker嵌入，簇代数结构允许通过突变在一组代数独立的Plücker坐标的最大集合之间移动。 Fioresi和Hacon研究了有限Grassmannian坐标环的一个特定余极限及其与Sato以及独立于Segal和Wilson引入的无限Grassmannian之间的联系，这些联系与Kadomtsev-Petiashvili (KP) 层次有关，这是一个具有孤立子解的无穷非线性偏微分方程集。 本文证明了这个环是一个具有由余极限构造诱导结构的无限秩簇代数。 更一般地，我们证明无限秩簇代数恰好是自然簇代数范畴中的归纳对象。 显示英文摘要

摘要： A prototypical examples of a cluster algebra is the coordinate ring of a finite Grassmannian: using the Pl\"ucker embedding the cluster algebra structure allows one to move between `maximal sets' of algebraically independent Pl\"ucker coordinates via mutations. Fioresi and Hacon studied a specific colimit of the coordinate rings of finite Grassmannians and its link with the infinite Grassmannian introduced by Sato and independently by Segal and Wilson in connection with the Kadomtsev-Petiashvili (KP) hierarchy, an infinite set of nonlinear partial differential equations which possess soliton solutions. In this article we prove that this ring is a cluster algebra of infinite rank with the structure induced by the colimit construction. More generally, we prove that cluster algebras of infinite rank are precisely the ind-objects of a natural category of cluster algebras.