E8 lattice
E656669
even unimodular lattice
integral lattice
lattice
positive-definite lattice
root lattice
sphere packing
The E8 lattice is an eight-dimensional, highly symmetric even unimodular lattice that plays a central role in Lie theory, sphere packing, and string theory.
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
even unimodular lattice
ⓘ
integral lattice ⓘ lattice ⓘ positive-definite lattice ⓘ root lattice ⓘ sphere packing ⓘ |
| associatedRootSystem | E8 root system ⓘ |
| automorphismGroup | Weyl group of type E8 NERFINISHED ⓘ |
| determinant | 1 ⓘ |
| dimension | 8 ⓘ |
| directSumWithE8AndD16Forms | Niemeier lattices NERFINISHED ⓘ |
| directSumWithItselfForms | E8⊕E8 lattice ⓘ |
| discriminant | 1 ⓘ |
| givesOptimalSpherePackingInDimension | 8 ⓘ |
| hasCoxeterNumber | 30 ⓘ |
| hasDynkinType | E8 ⓘ |
| hasNoRootsOfNorm | 1 ⓘ |
| hasRootsOfNorm | 2 ⓘ |
| hasRootSystemSize | 240 ⓘ |
| hasThetaSeries | weight4 modular form ⓘ |
| isBuildingBlockOf | Leech lattice NERFINISHED ⓘ |
| isEven | true ⓘ |
| isEvenUnimodular | true ⓘ |
| isEvenUnimodularPositiveDefiniteOfRankLessThan | 24 ⓘ |
| isGeneratedBy | E8 root system NERFINISHED ⓘ |
| isHighlySymmetric | true ⓘ |
| isIntegral | true ⓘ |
| isPositiveDefinite | true ⓘ |
| isRootLatticeOf | E8 Lie algebra NERFINISHED ⓘ |
| isSelfDual | true ⓘ |
| isUnimodular | true ⓘ |
| isUniqueEvenUnimodularLatticeOfRank | 8 ⓘ |
| kissingNumber | 240 ⓘ |
| minimalNorm | 2 ⓘ |
| numberOfMinimalVectors | 240 ⓘ |
| rank | 8 ⓘ |
| relatedTo |
Lie algebra of type E8
ⓘ
exceptional Lie group E8 NERFINISHED ⓘ |
| spherePackingDensity | highestKnownInDimension8 ⓘ |
| thetaSeriesIsModularFormFor | SL2(Z) ⓘ |
| usedIn |
E8×E8 heterotic string
NERFINISHED
ⓘ
Lie theory ⓘ conformal field theory ⓘ heterotic string theory NERFINISHED ⓘ lattice vertex operator algebras ⓘ sphere packing theory ⓘ string theory ⓘ |
| WeylGroup | Weyl group of type E8 NERFINISHED ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.