E7 (mathematics)
In mathematics, E7 is the name of several closely related Lie groups, linear algebraic groups or their Lie algebras e7, all of which have dimension 133; the same notation E7 is used for the corresponding root lattice, which has rank 7. The designation E7 comes from the Cartan–Killing classification of the complex simple Lie algebras, which fall into four infinite series labeled An, Bn, Cn, Dn, and five exceptional cases labeled E6, E7, E8, F4, and G2. The E7 algebra is thus one of the five exceptional cases.
The fundamental group of the (adjoint) complex form, compact real form, or any algebraic version of E7 is the cyclic group Z/2Z, and its outer automorphism group is the trivial group. The dimension of its fundamental representation is 56.
Read more about E7 (mathematics): Real and Complex Forms, E7 As An Algebraic Group, Important Subalgebras and Representations, Chevalley Groups of Type E7, Importance in Physics