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.
Statements (45)
| Predicate | Object |
|---|---|
| instanceOf |
Lie group
ⓘ
Lorentz group ⓘ matrix group ⓘ |
| actsOn | anti-de Sitter space AdS_d NERFINISHED ⓘ |
| actsTransitivelyOn | AdS_d ⓘ |
| appearsIn | AdS/CFT correspondence NERFINISHED ⓘ |
| 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) NERFINISHED ⓘ |
| 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) NERFINISHED ⓘ |
| hasLieAlgebra | so(2,d-1) ⓘ |
| hasMaximalCompactSubgroup | SO(2)×SO(d-1) NERFINISHED ⓘ |
| 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) NERFINISHED ⓘ |
| isRealFormOf | SO(d+1,ℂ) ⓘ |
| isRelatedGroup | Spin(2,d-1) ⓘ |
| isSemisimple | true ⓘ |
| isSimpleFor | d+1 ≥ 5 ⓘ |
| isSubgroupOf | O(2,d-1) ⓘ |
| isSymmetryGroupOf | AdS_d NERFINISHED ⓘ |
| isUsedIn |
conformal field theory
ⓘ
holographic dualities ⓘ string theory on AdS backgrounds ⓘ |
| preserves | quadratic form with two time-like and d-1 space-like directions ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.