Groups of extended affine Lie type

TL;DR

This paper constructs Steinberg groups linked to extended affine Lie algebras, demonstrating how their Weyl groups can be recovered as quotient groups, thus advancing the understanding of their algebraic structure.

Contribution

It introduces a novel construction of Steinberg groups for extended affine Lie algebras and relates their Weyl groups to quotient groups within this framework.

Findings

Weyl group recovered as a quotient of subgroups

Construction of Steinberg groups for extended affine Lie algebras

Connection to Kac-Moody groups

Abstract

We construct certain Steinberg groups associated to extended affine Lie algebras and their root systems. Then by the integration methods of Kac and Peterson for integrable Lie algebras, we associate a group to every tame extended affine Lie algebra. Afterwards, we show that the extended affine Weyl group of the ground Lie algebra can be recovered as a quotient group of two subgroups of the group associated to the underlying algebra similar to Kac-Moody groups.