Cluster algebras in algebraic Lie theory

TL;DR

This paper surveys recent developments in applying cluster algebra structures to coordinate rings of unipotent subgroups and cells in Kac-Moody groups, including their quantized versions.

Contribution

It provides a comprehensive overview of the construction and quantization of cluster algebra structures in algebraic Lie theory.

Findings

Cluster algebra structures are established on coordinate rings of unipotent subgroups.

Quantized versions of these cluster algebra structures are developed.

The survey highlights recent advances and open problems in the field.

Abstract

We survey some recent constructions of cluster algebra structures on coordinate rings of unipotent subgroups and unipotent cells of Kac-Moody groups. We also review a quantized version of these results.