Spin(2,d)
E590885
Spin(2,d) is the double-covering spin group of SO(2,d), serving as the relevant symmetry group for spinor fields in (d+1)-dimensional anti-de Sitter space.
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
Lie group
ⓘ
double cover ⓘ spin group ⓘ universal covering group ⓘ |
| actsOn | spinor fields on AdS_{d+1} ⓘ |
| containsSubgroup |
Spin(2)
NERFINISHED
ⓘ
Spin(d) ⓘ |
| covers | SO(2,d) NERFINISHED ⓘ |
| generalizes |
Spin(2,2) (AdS_{3} spin group)
NERFINISHED
ⓘ
Spin(2,3) (AdS_{4} spin group) NERFINISHED ⓘ Spin(2,4) (AdS_{5} spin group) ⓘ |
| hasCenter | \mathbb{Z}_{2} (for generic d) ⓘ |
| hasDimension | (d+2)(d+1)/2 ⓘ |
| hasFundamentalRepresentation | spinor representation ⓘ |
| hasLieAlgebra | \mathfrak{so}(2,d) ⓘ |
| hasMaximalCompactSubgroup | Spin(2)\times Spin(d) NERFINISHED ⓘ |
| hasProjectiveRepresentation | conformal group of d-dimensional Minkowski space ⓘ |
| hasRank | \min(2,d) ⓘ |
| hasSignature | (2,d) ⓘ |
| hasTopology | same as universal cover of SO(2,d)_{0} ⓘ |
| isCompact | false ⓘ |
| isConformalGroupOf | d-dimensional Minkowski space at the spin level ⓘ |
| isConnected | true ⓘ |
| isCoveringGroupOf | SO(2,d)_{0} NERFINISHED ⓘ |
| isDefinedAs | \{x\in Cl^{0}(2,d)\mid x V x^{-1}=V,\ \forall V\subset \mathbb{R}^{2,d}\} ⓘ |
| isDefinedOver | \mathbb{R} ⓘ |
| isDoubleCoverOf | SO(2,d) NERFINISHED ⓘ |
| isGlobalSymmetryOf | free spinor fields on AdS_{d+1} ⓘ |
| isIdentityComponentOf | Pin(2,d) NERFINISHED ⓘ |
| isIsometryGroupOf |
a space of signature (2,d) at the spin level
ⓘ
spin structure on AdS_{d+1} ⓘ |
| isLocallyIsomorphicTo | SO(2,d) NERFINISHED ⓘ |
| isNonAbelian | true ⓘ |
| isPartOf | AdS_{d+1} isometry supergroup in supersymmetric theories ⓘ |
| isRealFormOf | Spin(d+2,\mathbb{C}) ⓘ |
| isReductive | true ⓘ |
| isSemisimple | true ⓘ |
| isSimplyConnected | true ⓘ |
| isSubgroupOf |
Cl(2,d)^{\times}
ⓘ
Pin(2,d) ⓘ |
| isSymmetryGroupOf | spinor fields in (d+1)-dimensional anti-de Sitter space ⓘ |
| isUniversalCoverOf | SO(2,d)^{ ext{connected}} ⓘ |
| isUsedIn |
AdS/CFT correspondence
NERFINISHED
ⓘ
higher-spin gauge theories on AdS_{d+1} ⓘ supergravity on AdS_{d+1} NERFINISHED ⓘ |
| isUsedToDefine | spin structures on AdS_{d+1} ⓘ |
| preserves | quadratic form of signature (2,d) ⓘ |
| relatesTo | Clifford algebra Cl(2,d) NERFINISHED ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.