Example of categorification of a cluster algebra

Abstract

We present here two detailed examples of additive categorifications of the cluster algebra structure of a coordinate ring of a maximal unipotent subgroup of a simple Lie group. The first one is of simply-laced type ($A_3$) and relies on an article by Geiß, Leclerc and Schröer. The second is of non simply-laced type ($C_2$) and relies on an article by the author of this note. This is aimed to be accessible, specially for people who are not familiar with this subject.

13 pages, 44th Symposium on Ring and Representation Theory (Japan)