About: E7 (mathematics)

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In mathematics, E7 is the name of several closely related Lie groups, linear algebraic groups or their Lie algebras e7, all of which have dimension 133; the same notation E7 is used for the corresponding root lattice, which has rank 7. The designation E7 comes from the Cartan–Killing classification of the complex simple Lie algebras, which fall into four infinite series labeled An, Bn, Cn, Dn, and five exceptional cases labeled E6, E7, E8, F4, and G2. The E7 algebra is thus one of the five exceptional cases.

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  • In mathematics, E7 is the name of several closely related Lie groups, linear algebraic groups or their Lie algebras e7, all of which have dimension 133; the same notation E7 is used for the corresponding root lattice, which has rank 7. The designation E7 comes from the Cartan–Killing classification of the complex simple Lie algebras, which fall into four infinite series labeled An, Bn, Cn, Dn, and five exceptional cases labeled E6, E7, E8, F4, and G2. The E7 algebra is thus one of the five exceptional cases. The fundamental group of the (adjoint) complex form, compact real form, or any algebraic version of E7 is the cyclic group Z/2Z, and its outer automorphism group is the trivial group. The dimension of its fundamental representation is 56. (en)
  • En mathématiques, E7 est le nom d'un groupe de Lie complexe de type exceptionnel. Son algèbre de Lie est notée . E7 est de rang 7 et de dimension 133. Le groupe fondamental de sa forme compacte est le groupe cyclique Z2. sa représentation fondamentale est de dimension 56. La forme compacte réelle de E7 est le groupe d'isométries d'une variété riemannienne de dimension 64 appelée plan projectif quateroctionique. Ce nom vient du fait qu'il peut être construit en utilisant une algèbre qui est construite comme produit tensoriel des quaternions avec les octonions. Ce type de construction est analysé en détail par Hans Freudenthal et Jacques Tits dans leur construction du (en). (fr)
  • 리 군론에서 E7은 복소수 예외적 단순 리 군의 하나이다. 133차원이며, 예외적 단순 리 군 가운데 E8 다음으로 두 번째로 크다. (ko)
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  • 리 군론에서 E7은 복소수 예외적 단순 리 군의 하나이다. 133차원이며, 예외적 단순 리 군 가운데 E8 다음으로 두 번째로 크다. (ko)
  • In mathematics, E7 is the name of several closely related Lie groups, linear algebraic groups or their Lie algebras e7, all of which have dimension 133; the same notation E7 is used for the corresponding root lattice, which has rank 7. The designation E7 comes from the Cartan–Killing classification of the complex simple Lie algebras, which fall into four infinite series labeled An, Bn, Cn, Dn, and five exceptional cases labeled E6, E7, E8, F4, and G2. The E7 algebra is thus one of the five exceptional cases. (en)
  • En mathématiques, E7 est le nom d'un groupe de Lie complexe de type exceptionnel. Son algèbre de Lie est notée . E7 est de rang 7 et de dimension 133. Le groupe fondamental de sa forme compacte est le groupe cyclique Z2. sa représentation fondamentale est de dimension 56. (fr)
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  • E7 (mathematics) (en)
  • E7 (mathématiques) (fr)
  • E₇ (ko)
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