About: E8 lattice

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In mathematics, the E8 lattice is a special lattice in R8. It can be characterized as the unique positive-definite, even, unimodular lattice of rank 8. The name derives from the fact that it is the root lattice of the E8 root system.

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rdf:type	architectural structure yago:Abstraction100002137 yago:Form106290637 yago:LanguageUnit106284225 yago:Part113809207 yago:Relation100031921 yago:Word106286395 yago:WikicatQuadraticForms
rdfs:label	E8 lattice (en) E8 격자 (ko) E8-rooster (nl) Решётка E8 (ru) Ґратка E8 (uk)
rdfs:comment	수학에서 E8 격자는 의 유일한 양의 정부호 짝 유니모듈러 격자이다. 이름은 E8 근계의 근 격자라는 사실에서 지어졌다. E8 격자의 노름은 8개의 변수에서 양의 정부호 짝 유니모듈러 이차 형식이며, 역으로 이러한 이차 형식은 계수 8의 양의 정부호 짝 유니모듈러 격자를 구성하는 데 사용할 수 있다. 이러한 이차 형식의 존재는 1867년에 헨리 존 스티븐 스미스에 의해 처음으로 제시되었으며, 이 이차 형식의 첫 번째 명시적 구성은 1873년에 과 에 의해 주어졌다. E8 격자는 1900년경 격자 자체의 기하학을 최초로 연구한 의 이름을 따서 고셋 격자라고도 한다. (ko) In de wiskunde is het E8-rooster een speciaal rooster in R8. Het kan worden gekarakteriseerd als het unieke positief-definiete, even, unimodulair rooster van rang 8. De naam is afgeleid uit het feit dat het het wortelrooster van het E8-wortelsysteem is. (nl) Решётка Е8, или решётка Коркина — Золотарёва, — корневая решётка группы Е8. Она реализует в размерности 8: * Максимально возможное контактное число; * Плотнейшую упаковку шаров. Обычно обозначается , также как и группa Е8. (ru) Ґратка Е8 або ґратка Коркінас — Золотарьова — коренева ґратка групи . Вона реалізує в розмірності 8: * найбільше можливе контактне число; * найщільніше пакування куль. Зазвичай позначається , як і група . (uk) In mathematics, the E8 lattice is a special lattice in R8. It can be characterized as the unique positive-definite, even, unimodular lattice of rank 8. The name derives from the fact that it is the root lattice of the E8 root system. (en)
dct:subject	E8 (mathematics) Quadratic forms Lattice points
Wikipage page ID	1800359 (xsd:integer)
Wikipage revision ID	1096575356 (xsd:integer)
Link from a Wikipage to another Wikipage	Determinant Algebra over a field Holomorphic function Permutation E8 (mathematics) E8 manifold E8 polytope Quadratic forms Maryna Viazovska Mathematics Smooth structure Subring Eisenstein series Lattice points Modular form Convex hull Theta function Root lattice Leech lattice Local maximum String theory Half-integer Hamming weight Symmetry group 5 21 honeycomb 8-orthoplex 8-simplex Divisor function Dual lattice Coxeter-Dynkin diagram Hadamard matrix Lattice (group) Linear code Aleksandr Korkin 4-manifold E8 (mathematics) Quadratic form Upper half-plane Reflection (mathematics) Hamming code Hans Frederick Blichfeldt Hexadecimal Intersection form (4-manifold) Isomorphic Coxeter group Vertex figure Triangulation (topology) Automorphism group H. S. M. Coxeter H. J. S. Smith Maximal order Integer Michael Freedman Octonion Orbit (group theory) Order (group theory) Orthogonal group Root system Unimodular lattice Niemeier lattice Face (geometry) Facet (geometry) Yegor Ivanovich Zolotarev Thorold Gosset Kissing number problem Weyl group Uniform honeycomb Delaunay cell Upper triangular matrix Bosonic string Self-dual code Heterotic string Nonassociative ring Fundamental parallelotope Discrete subgroup Block diagonal matrix Superstring

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