Chevalley bases for extended affine Lie algebras

Abstract

Claude Chevalley provided a basis for a {finite dimensional} simple complex Lie algebra called the Chevalley basis. This basis has the distinguishing property that all the structure constants are integers. Chevalley groups, which are similar to Lie groups but over finite fields, can be constructed using these bases. Parallel results also hold in affine Lie algebras. We develop a uniform theory of Chevalley bases for extended affine Lie algebras of an arbitrary type consistent with the ordinary theory for finite and affine cases. It explains how a Chevalley basis for a finite-dimensional simple Lie algebra or an affine Lie algebra can be extended to one for the covering extended affine Lie algebras.