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: unitary group U(n+1) | Statement: [Fubini–Study form, isInvariantUnder, unitary group U(n+1)]

Target entity: unitary group U(n+1)
Context triple: [Fubini–Study form, isInvariantUnder, unitary group U(n+1)]

• A. special unitary group SU(n)
  The special unitary group SU(n) is a fundamental compact Lie group consisting of n×n unitary matrices with determinant 1, central in mathematics and physics, especially in quantum theory and gauge symmetries.
• B. U(1)
  U(1) is the group of complex numbers with absolute value 1 under multiplication, commonly representing the symmetry group of electromagnetism and other abelian gauge theories.
• C. general linear group GL(n,C)
  The general linear group GL(n,ℂ) is the Lie group consisting of all invertible n×n complex matrices under matrix multiplication, fundamental in linear algebra and representation theory.
• D. projective special unitary group PSU(2)
  The projective special unitary group PSU(2) is a simple Lie group that can be realized as the group of orientation-preserving rotations of three-dimensional Euclidean space.
• E. special linear group SL(n,C)
  The special linear group SL(n,ℂ) is the Lie group of n×n complex matrices with determinant 1, fundamental in representation theory, geometry, and many areas of modern mathematics and physics.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: unitary group U(n+1)
Target entity description: The unitary group U(n+1) is the Lie group of all (n+1)×(n+1) complex matrices that preserve the standard Hermitian inner product, playing a central role in geometry, representation theory, and quantum mechanics.

• A. special unitary group SU(n)
  The special unitary group SU(n) is a fundamental compact Lie group consisting of n×n unitary matrices with determinant 1, central in mathematics and physics, especially in quantum theory and gauge symmetries.
• B. U(1)
  U(1) is the group of complex numbers with absolute value 1 under multiplication, commonly representing the symmetry group of electromagnetism and other abelian gauge theories.
• C. general linear group GL(n,C)
  The general linear group GL(n,ℂ) is the Lie group consisting of all invertible n×n complex matrices under matrix multiplication, fundamental in linear algebra and representation theory.
• D. projective special unitary group PSU(2)
  The projective special unitary group PSU(2) is a simple Lie group that can be realized as the group of orientation-preserving rotations of three-dimensional Euclidean space.
• E. special linear group SL(n,C)
  The special linear group SL(n,ℂ) is the Lie group of n×n complex matrices with determinant 1, fundamental in representation theory, geometry, and many areas of modern mathematics and physics.
• F. None of above. chosen