Weyl groups of some hyperbolic Kac-Moody algebras

TL;DR

This paper explores the structure of Weyl groups associated with certain hyperbolic Kac-Moody algebras using Clifford algebra and Vahlen groups, providing new insights into their algebraic properties.

Contribution

It introduces a novel approach to studying Weyl groups of hyperbolic Kac-Moody algebras via Clifford algebra and Vahlen groups, extending understanding of their algebraic structure.

Findings

Weyl groups of hyperbolic Kac-Moody algebras are characterized using Clifford algebras.

The paper establishes a connection between Vahlen groups and these Weyl groups.

New algebraic properties of these Weyl groups are identified.

Abstract

We use the theory of Clifford algebras and Vahlen groups to study Weyl groups of hyperbolic Kac-Moody algebras T_n^{++}, obtained by a process of double extension from a Cartan matrix of finite type T_n, whose corresponding generalized Cartan matrices are symmetric.