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: Lie group theory | Statement: [Erlangen Program, influencedField, Lie group theory]

Target entity: Lie group theory
Context triple: [Erlangen Program, influencedField, Lie group theory]

• A. Lie theory chosen
  Lie theory is a branch of mathematics that studies continuous symmetry through Lie groups and Lie algebras, with deep applications in geometry, analysis, and theoretical physics.
• B. Lie group
  A Lie group is a mathematical structure that is both a smooth manifold and a group, where the group operations are differentiable and used to study continuous symmetries.
• C. Lie pseudogroup
  A Lie pseudogroup is a collection of local diffeomorphisms on a manifold that is closed under composition, inversion, and restriction, generalizing the concept of a Lie group to transformations defined only locally.
• D. Theorie der Transformationsgruppen
  Theorie der Transformationsgruppen is Sophus Lie’s foundational multi-volume work that established the theory of continuous transformation groups, now known as Lie groups, and their applications to differential equations and geometry.
• E. Erlangen Program
  The Erlangen Program is Felix Klein’s influential 1872 framework that classifies and studies geometries based on their underlying symmetry groups and transformation properties.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.