Triple

Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).

Phrase: affine Weyl group | Statement: [affine Lie algebras, hasInvariant, affine Weyl group]

Target entity: affine Weyl group
Context triple: [affine Lie algebras, hasInvariant, affine Weyl group]

• A. Weyl group
  A Weyl group is a finite reflection group associated with a root system that encodes the symmetries of Lie algebras and Lie groups in representation theory and geometry.
• B. Coxeter group
  A Coxeter group is an abstract group generated by reflections across hyperplanes, fundamental in the classification and study of regular polytopes, tessellations, and symmetries in geometry and algebra.
• C. affine Lie algebras
  Affine Lie algebras are infinite-dimensional extensions of finite-dimensional simple Lie algebras that play a central role in representation theory, conformal field theory, and the study of exactly solvable models in mathematical physics.
• D. 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.
• E. Weyl vector
  The Weyl vector is a distinguished element in the weight space of a semisimple Lie algebra, defined as half the sum of all positive roots and playing a central role in representation theory and the Weyl character formula.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: affine Weyl group
Target entity description: An affine Weyl group is an infinite Coxeter group generated by reflections associated with an affine root system, playing a central role in the structure and representation theory of affine Lie algebras.

• A. Weyl group
  A Weyl group is a finite reflection group associated with a root system that encodes the symmetries of Lie algebras and Lie groups in representation theory and geometry.
• B. Coxeter group
  A Coxeter group is an abstract group generated by reflections across hyperplanes, fundamental in the classification and study of regular polytopes, tessellations, and symmetries in geometry and algebra.
• C. affine Lie algebras
  Affine Lie algebras are infinite-dimensional extensions of finite-dimensional simple Lie algebras that play a central role in representation theory, conformal field theory, and the study of exactly solvable models in mathematical physics.
• D. 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.
• E. Weyl vector
  The Weyl vector is a distinguished element in the weight space of a semisimple Lie algebra, defined as half the sum of all positive roots and playing a central role in representation theory and the Weyl character formula.
• F. None of above. chosen