unitary group U(n+1)
E1531306
UNEXPLORED
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.
All labels observed (1)
| Label | Occurrences |
|---|---|
| unitary group U(n+1) canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T22328555 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: unitary group U(n+1) Context triple: [Fubini–Study form, isInvariantUnder, unitary group U(n+1)]
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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.
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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.
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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.
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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.
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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.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
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
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.