F4 (mathematics)
In mathematics, F4 is the name of a Lie group and also its Lie algebra . It is one of the five exceptional simple Lie groups. F4 has rank 4 and dimension 52. Its center is the trivial subgroup. Its outer automorphism group is the trivial group. Its fundamental representation is 26-dimensional.
Algebra 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.
Roots of F4
:
Simple roots
: -
Weyl/Coxeter group
Its Weyl/Coxeter group is the symmetry group of the 24-cell.
:
F4 lattice
The F4 lattice is a four dimensional body-centered cubic lattice (i.e. the union of two hypercubic lattices, each lying in the center of the other). They form a ring called the Hurwitz quaternion ring.
|
|
