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 | Statement: [Sophus Lie, hasNameInMathematics, Lie group]

Target entity: Lie group
Context triple: [Sophus Lie, hasNameInMathematics, Lie group]

• A. 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.
• B. 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.
• 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 subgroup
  A Lie subgroup is a subgroup of a Lie group that is itself a Lie group and an embedded submanifold, inheriting compatible smooth and group structures from the ambient Lie group.
• E. Lorentz group
  The Lorentz group is the mathematical group of spacetime symmetries in special relativity, consisting of all rotations and boosts that preserve the Minkowski spacetime interval.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target predicate: hasNameInMathematics
Context triple: [Sophus Lie, hasNameInMathematics, Lie group]

• A. hasTheoremNamedAfter
  Indicates that a theorem is named in honor of or after a particular person or entity.
• B. hasMatha
  Indicates a relationship where one entity possesses, is associated with, or is characterized by a specific matha (monastic institution or religious seat).
• C. nameOf chosen
  Indicates that one entity is the name or designation of another entity.
• D. associatedMatha
  Indicates a relationship where one entity is linked or affiliated with a particular matha (monastic or religious institution).
• E. hasNotableMathematician
  Indicates that an entity is associated with or linked to a mathematician who is considered notable or distinguished.
• F. None of above.