Chevalley bases for extended affine Lie algebras

Chevalley provided a basis, called a Chevalley basis, for a simple complex Lie algebra. 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 for affine Lie algebras. We develop a uniform theory of Chevalley bases for extended affine Lie algebras of 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 a Chevalley basis for the covering extended affine Lie algebras.