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: Möbius group of the n-sphere | Statement: [Lie sphere group, hasSubgroup, Möbius group of the n-sphere]

Target entity: Möbius group of the n-sphere
Context triple: [Lie sphere group, hasSubgroup, Möbius group of the n-sphere]

• A. Möbius geometry
  Möbius geometry is a branch of geometry that studies properties of figures invariant under Möbius (conformal) transformations of the extended complex plane or higher-dimensional spheres.
• B. Möbius transformations
  Möbius transformations are conformal automorphisms of the extended complex plane represented by fractional linear functions that map circles and lines to circles and lines.
• C. Lie sphere group
  The Lie sphere group is the continuous symmetry group that preserves the incidence and contact relations of spheres, planes, and points in Lie sphere geometry.
• D. Riemann sphere
  The Riemann sphere is the complex plane plus a point at infinity, forming a one-dimensional complex manifold topologically equivalent to a sphere and used to study meromorphic functions and complex analysis.
• E. Between the Torus and the Sphere
  "Between the Torus and the Sphere" is a large-scale steel sculpture by Richard Serra, created as part of his immersive installation series exploring time, space, and viewer movement.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Möbius group of the n-sphere
Target entity description: The Möbius group of the n-sphere is the group of all conformal diffeomorphisms of the n-dimensional sphere, generated by inversions, rotations, translations, and dilations.

• A. Möbius geometry chosen
  Möbius geometry is a branch of geometry that studies properties of figures invariant under Möbius (conformal) transformations of the extended complex plane or higher-dimensional spheres.
• B. Möbius transformations
  Möbius transformations are conformal automorphisms of the extended complex plane represented by fractional linear functions that map circles and lines to circles and lines.
• C. Lie sphere group
  The Lie sphere group is the continuous symmetry group that preserves the incidence and contact relations of spheres, planes, and points in Lie sphere geometry.
• D. Riemann sphere
  The Riemann sphere is the complex plane plus a point at infinity, forming a one-dimensional complex manifold topologically equivalent to a sphere and used to study meromorphic functions and complex analysis.
• E. Between the Torus and the Sphere
  "Between the Torus and the Sphere" is a large-scale steel sculpture by Richard Serra, created as part of his immersive installation series exploring time, space, and viewer movement.
• F. None of above.