Chevalley basis

A Chevalley basis is a special set of vectors used to study complex Lie algebras, which are mathematical structures capturing symmetry. This basis simplifies calculations and reveals the algebra’s properties by choosing elements with nice, predictable interaction rules. Essentially, it breaks down a complex symmetry structure into basic "building blocks" that work well together, making advanced mathematical analysis more manageable. The Chevalley basis is especially useful for understanding both the algebra over real or complex numbers and its related geometric and algebraic structures.