F4, F.IV, F04, F 4, F.4 or F-4 may refer to:
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.
The Dynkin diagram for F4 is .
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).