Closed sets of real roots in Kac-Moody root systems

TL;DR

This paper provides a comprehensive classification of all closed sets of real roots within Kac-Moody root systems, advancing understanding of their structure.

Contribution

It offers the first complete description of closed sets of real roots in Kac-Moody root systems, filling a key gap in the literature.

Findings

Complete classification of closed sets of real roots

Clarification of the structure of Kac-Moody root systems

Foundation for further algebraic and geometric studies

Abstract

In this note, we provide a complete description of the closed sets of real roots in a Kac-Moody root system.