Integral structures in extended affine Lie algebras

TL;DR

This paper develops integral structures for extended affine Lie algebras, generalizing Chevalley automorphisms, enabling the definition of associated groups over arbitrary fields.

Contribution

It introduces a method to construct integral forms in extended affine Lie algebras using generalized Chevalley automorphisms, expanding their algebraic and group-theoretic applications.

Findings

Integral structures constructed for cores of extended affine Lie algebras

Generalization of Chevalley automorphisms to this context

Groups of extended affine Lie type defined over arbitrary fields

Abstract

We construct certain integral structures for the cores of reduced tame extended affine Lie algebras of rank at least 2. One of the main tools to achieve this is a generalization of Chevalley automorphisms in the context of extended affine Lie algebras. As an application, groups of extended affine Lie type associated to the adjoint representation are defined over arbitrary fields.