Chevalley groups

Chevalley groups are a class of mathematical structures that arise from algebraic groups associated with Lie algebras, constructed over finite fields. They serve as central objects in group theory, combining continuous symmetry concepts (Lie groups) with discrete settings (finite fields). These groups have applications in areas like coding theory, cryptography, and combinatorics. In essence, Chevalley groups provide a systematic way to generate highly symmetric, finite groups from the algebraic structures underlying symmetry in geometry and physics.