Laurent Demonet, Osamu Iyama
Published 2015-03-09Version 1
In this article, we describe a categorification of the cluster algebra structure of multi-homogeneous coordinate rings of partial flag varieties of type $A$ and $D$ using Cohen-Macaulay modules over orders. To achieve this, we construct several equivalences of categories, relating Cohen-Macaulay modules over an order $A$ to finitely generated modules over certain finite length algebras obtained as quotient of $A$ by an idempotent.
Example of categorification of a cluster algebra
A categorification of Grassmannian cluster algebras
Unistructurality of cluster algebras of type {\widetilde{\mathbb{A}}}
![QR code for arXiv:1503.02362 [math.RT]](http://oss.arxitics.com/images/favicon.svg)