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 actions | Statement: [Lie sphere geometry, basedOn, Lie group actions]

Target entity: Lie group actions
Context triple: [Lie sphere geometry, basedOn, Lie group actions]

• A. Lie theory
  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 chosen
  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. Lie algebras
  Lie algebras are algebraic structures used to study continuous symmetries, especially those arising from Lie groups, via a linearized, infinitesimal perspective.
• E. 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.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.