SO(2,d-1)
E590883
SO(2,d-1) is the non-compact Lorentz group in (d+1) dimensions that serves as the symmetry group of d-dimensional anti-de Sitter space and plays a central role in AdS/CFT correspondence.
All labels observed (1)
| Label | Occurrences |
|---|---|
| SO(2,d-1) canonical | 2 |
How this entity was disambiguated
This entity first appeared as the object of triple T6396948 — 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: SO(2,d-1) Context triple: [anti-de Sitter space, hasIsometryGroup, SO(2,d-1)]
-
A.
AdS isometry group SO(2,d)
The AdS isometry group SO(2,d) is the spacetime symmetry group of (d+1)-dimensional anti-de Sitter space, matching the conformal symmetry group of the dual d-dimensional field theory in the AdS/CFT correspondence.
-
B.
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.
-
C.
special orthogonal group SO(n)
The special orthogonal group SO(n) is the group of all n×n real rotation matrices with determinant 1, representing orientation-preserving isometries of n-dimensional Euclidean space that fix the origin.
-
D.
SL(2,C)
SL(2,C) is the complex special linear group of 2×2 matrices with determinant 1, which serves as the double cover and spinor representation group of the proper orthochronous Lorentz group in four-dimensional spacetime.
-
E.
rotation group SU(2)
The rotation group SU(2) is the Lie group of 2×2 unitary matrices with determinant 1 that serves as the double cover of the three-dimensional rotation group SO(3) and underlies the quantum theory of angular momentum and spin.
- 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: SO(2,d-1) Target entity description: SO(2,d-1) is the non-compact Lorentz group in (d+1) dimensions that serves as the symmetry group of d-dimensional anti-de Sitter space and plays a central role in AdS/CFT correspondence.
-
A.
AdS isometry group SO(2,d)
The AdS isometry group SO(2,d) is the spacetime symmetry group of (d+1)-dimensional anti-de Sitter space, matching the conformal symmetry group of the dual d-dimensional field theory in the AdS/CFT correspondence.
-
B.
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.
-
C.
special orthogonal group SO(n)
The special orthogonal group SO(n) is the group of all n×n real rotation matrices with determinant 1, representing orientation-preserving isometries of n-dimensional Euclidean space that fix the origin.
-
D.
SL(2,C)
SL(2,C) is the complex special linear group of 2×2 matrices with determinant 1, which serves as the double cover and spinor representation group of the proper orthochronous Lorentz group in four-dimensional spacetime.
-
E.
rotation group SU(2)
The rotation group SU(2) is the Lie group of 2×2 unitary matrices with determinant 1 that serves as the double cover of the three-dimensional rotation group SO(3) and underlies the quantum theory of angular momentum and spin.
- F. None of above. chosen
Statements (45)
| Predicate | Object |
|---|---|
| instanceOf |
Lie group
ⓘ
Lorentz group ⓘ matrix group ⓘ |
| actsOn |
anti-de Sitter space AdS_d
ⓘ
linked to:
anti-de Sitter space
|
| actsTransitivelyOn | AdS_d ⓘ |
| appearsIn | AdS/CFT correspondence ⓘ |
| definedAs | group of real (d+1)×(d+1) matrices preserving a bilinear form of signature (2,d-1) with determinant 1 ⓘ |
| hasAbbreviation | SO(2,d-1) ⓘ |
| hasCartanDecomposition | K⊕P with K ≅ so(2)⊕so(d-1) ⓘ |
| hasCasimirOperators | quadratic and higher-order Casimirs used to label representations ⓘ |
| hasCenter | finite center depending on d ⓘ |
| hasDeterminantCondition | determinant equal to 1 ⓘ |
| hasDimension | (d+1)d/2 ⓘ |
| hasFullName | special orthogonal group of signature (2,d-1) ⓘ |
| hasLieAlgebra | so(2,d-1) ⓘ |
| hasMaximalCompactSubgroup | SO(2)×SO(d-1) ⓘ |
| hasPhysicalInterpretation | generalized Lorentz group with two time directions and d-1 space directions ⓘ |
| hasProperty |
non-amenable
ⓘ
non-compact but not nilpotent ⓘ real reductive group ⓘ unimodular ⓘ |
| hasRank | floor((d+1)/2) ⓘ |
| hasRealFormOf | so(d+1,ℂ) ⓘ |
| hasRole |
conformal symmetry of boundary CFT in AdS/CFT
ⓘ
global symmetry of AdS_d spacetime ⓘ |
| hasSignature | (2,d-1) ⓘ |
| hasTypeInCartanClassification | B_n or D_n depending on d+1 ⓘ |
| hasUnitaryRepresentationsUsedIn | classification of fields on AdS_d ⓘ |
| hasUniversalCover | Spin(2,d-1) ⓘ |
| isConformalGroupOf | (d-1)-dimensional Minkowski space up to coverings ⓘ |
| isConnectedComponentOf | O(2,d-1) ⓘ |
| isIsometryGroupOf | d-dimensional anti-de Sitter space ⓘ |
| isIsomorphicTo |
SO(2,3) for d=4
ⓘ
SO(2,4) for d=5 ⓘ |
| isNonCompactVersionOf |
SO(d+1)
ⓘ
linked to:
special orthogonal group SO(n)
|
| isRealFormOf | SO(d+1,ℂ) ⓘ |
| isRelatedGroup | Spin(2,d-1) ⓘ |
| isSemisimple | true ⓘ |
| isSimpleFor | d+1 ≥ 5 ⓘ |
| isSubgroupOf | O(2,d-1) ⓘ |
| isSymmetryGroupOf | AdS_d ⓘ |
| isUsedIn |
conformal field theory
ⓘ
holographic dualities ⓘ string theory on AdS backgrounds ⓘ |
| preserves | quadratic form with two time-like and d-1 space-like directions ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: SO(2,d-1) Description of subject: SO(2,d-1) is the non-compact Lorentz group in (d+1) dimensions that serves as the symmetry group of d-dimensional anti-de Sitter space and plays a central role in AdS/CFT correspondence.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.