Work

Chevalley bases for extended affine Lie algebras

Year: 2026

Type: article

Abstract: 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.

Source: Journal of Algebra and Its Applications

DOI: 10.1142/s0219498826400049

Author: S. Azam

Institutions: University of Isfahan, Institute for Research in Fundamental Sciences

Language: English

Topic: Advanced Topics in Algebra

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Iran National Science Foundation

Award: G6345885809