Chevalley basis

Target entity: Chevalley basis
Context triple: [Chevalley groups, constructedUsing, Chevalley basis]

• A. Chevalley groups
  Chevalley groups are a broad class of linear algebraic groups constructed over arbitrary fields that generalize classical Lie groups and play a central role in the classification of finite simple groups.
• B. Chevalley
  Chevalley is a French surname most prominently associated with Claude Chevalley, a influential 20th-century mathematician known for his work in algebra and group theory.
• C. Cartan subalgebras
  Cartan subalgebras are maximal abelian subalgebras of a Lie algebra consisting of semisimple elements, fundamental for classifying and understanding the structure of Lie algebras.
• D. Jordan–Chevalley decomposition
  The Jordan–Chevalley decomposition is a fundamental result in linear algebra and representation theory that expresses a linear operator (or matrix) as the sum or product of commuting semisimple and nilpotent parts.
• E. Gelfand–Tsetlin basis
  The Gelfand–Tsetlin basis is a canonical, combinatorially defined basis for representations of certain Lie algebras and groups, particularly used in the representation theory of GL(n) and related structures.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Chevalley basis
Target entity description: A Chevalley basis is a specially chosen basis of a semisimple Lie algebra with integral structure constants, enabling the uniform construction of Lie groups and algebraic groups over arbitrary fields.

• A. Chevalley groups
  Chevalley groups are a broad class of linear algebraic groups constructed over arbitrary fields that generalize classical Lie groups and play a central role in the classification of finite simple groups.
• B. Chevalley
  Chevalley is a French surname most prominently associated with Claude Chevalley, a influential 20th-century mathematician known for his work in algebra and group theory.
• C. Cartan subalgebras
  Cartan subalgebras are maximal abelian subalgebras of a Lie algebra consisting of semisimple elements, fundamental for classifying and understanding the structure of Lie algebras.
• D. Jordan–Chevalley decomposition
  The Jordan–Chevalley decomposition is a fundamental result in linear algebra and representation theory that expresses a linear operator (or matrix) as the sum or product of commuting semisimple and nilpotent parts.
• E. Gelfand–Tsetlin basis
  The Gelfand–Tsetlin basis is a canonical, combinatorially defined basis for representations of certain Lie algebras and groups, particularly used in the representation theory of GL(n) and related structures.
• F. None of above. chosen