Lie algebras

Satake diagram

In the mathematical study of Lie algebras and Lie groups, a Satake diagram is a generalization of a Dynkin diagram introduced by Satake whose configurations classify simple Lie algebras over the field of real numbers. The Satake diagrams associated to a Dynkin diagram classify real forms of the complex Lie algebra corresponding to the Dynkin diagram. More generally, the Tits index or Satake–Tits diagram of a reductive algebraic group over a field is a generalization of the Satake diagram to arbitrary fields, introduced by Tits, that reduces the classification of reductive algebraic groups to that of anisotropic reductive algebraic groups. Satake diagrams are not the same as Vogan diagrams of a Lie group, although they look similar. (Wikipedia).

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Related pages

Cartan decomposition | Reductive group | Split Lie algebra | Lie group | Galois cohomology | Dynkin diagram | Compact Lie algebra | Algebraic group | Vogan diagram | Mathematics | Field (mathematics) | Linear algebraic group | Real number | Cartan subalgebra | Lie algebra | Real form (Lie theory) | Semisimple Lie algebra | List of irreducible Tits indices