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- Q869077 subject Q7585268.
- Q869077 subject Q8805755.
- Q869077 abstract "In mathematics, F4 is the name of a Lie group and also its Lie algebra f4. It is one of the five exceptional simple Lie groups. F4 has rank 4 and dimension 52. The compact form is simply connected and its outer automorphism group is the trivial group. Its fundamental representation is 26-dimensional.The compact real form of F4 is the isometry group of a 16-dimensional Riemannian manifold known as the octonionic projective plane OP2. This can be seen systematically using a construction known as the magic square, due to Hans Freudenthal and Jacques Tits.There are 3 real forms: a compact one, a split one, and a third one. They are the isometry groups of the three real Albert algebras.The F4 Lie algebra may be constructed by adding 16 generators transforming as a spinor to the 36-dimensional Lie algebra so(9), in analogy with the construction of E8.In older books and papers, F4 is sometimes denoted by E4.".
- Q869077 thumbnail Dynkin_diagram_F4.png?width=300.
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- Q869077 wikiPageWikiLink Q8805755.
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- Q869077 comment "In mathematics, F4 is the name of a Lie group and also its Lie algebra f4. It is one of the five exceptional simple Lie groups. F4 has rank 4 and dimension 52. The compact form is simply connected and its outer automorphism group is the trivial group. Its fundamental representation is 26-dimensional.The compact real form of F4 is the isometry group of a 16-dimensional Riemannian manifold known as the octonionic projective plane OP2.".
- Q869077 label "F4 (mathematics)".
- Q869077 depiction Dynkin_diagram_F4.png.