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: Lorentz group | Statement: [Poincaré group, isSemidirectProductOf, Lorentz group]

Target entity: Lorentz group
Context triple: [Poincaré group, isSemidirectProductOf, Lorentz group]

• A. Lorentz group chosen
  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.
• B. Poincaré group
  The Poincaré group is the fundamental symmetry group of special relativity, combining spacetime translations with Lorentz transformations in four-dimensional Minkowski space.
• C. Galilean group
  The Galilean group is the mathematical group of spacetime transformations—comprising translations, rotations, and Galilean boosts—that characterize the symmetries of classical Newtonian mechanics.
• D. 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.
• E. Euclidean group
  The Euclidean group is the group of all distance-preserving transformations of Euclidean space, consisting of rotations, reflections, and translations.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target predicate: isSemidirectProductOf
Context triple: [Poincaré group, isSemidirectProductOf, Lorentz group]

• A. isNonAbelian
  Indicates that the operation or structure in question does not satisfy commutativity, so the order of applying the operation matters.
• B. hasAdditiveGroupIsomorphicTo
  Indicates that the additive group structure of one algebraic object is isomorphic (structure-preserving bijection exists) to the additive group structure of another.
• C. usesSymmetryGroup
  Indicates that one entity employs or is based on a particular symmetry group in its structure, behavior, or formulation.
• D. isCommutative
  Indicates that the result of applying an operation to two entities does not depend on their order (i.e., a ∘ b = b ∘ a).
• E. hasIsometryGroup
  Indicates that one entity possesses or is associated with a particular isometry group describing all distance-preserving transformations of that entity.
• F. None of above. chosen