F4
F4, F.IV, F04, F 4, F.4 or F-4 may refer to:
Aircraft
Art, entertainment, and media
Companies
Fictional entities
Music
F4 (mathematics)
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.
Algebra
Dynkin diagram
The Dynkin diagram for F4 is 
.
Weyl/Coxeter group
F4 (paper)
F4 is a paper format of size 210 mm × 330 mm (8.27 in × 12.99 in). Although metric, based on the A4 paper size, and named to suggest that it is part of the official ISO 216 paper sizes, it appears to be only a de facto standard.
It may be referred to as "foolscap" or "folio" because of its similarity to the traditional Foolscap folio size of 8 1⁄2 by 13 1⁄2 inches (215.9 mm × 342.9 mm).
