E8 (mathematics)
In mathematics, E_{8} is the name of a Lie group and also its Lie algebra. It is the largest of the five exceptional simple Lie groups. It is also one of the simply laced groups. E_{8} has rank 8 and dimension 248. Its fundamental representation is the 248-dimensional adjoint.
The Dynkin diagram of the E_{8} algebra is
One can construct the group as a symmetry group of the Lie algebra. This algebra has a 120-dimensional subalgebra generated by as well as 128 new generators that transform as a Weyl-Majorana spinor of . These statements determine the commutators
- ,
This group frequently appears in string theory and supergravity, for example as the U-duality group of supergravity on an eight-torus (a noncompact version), or as a part of the gauge group of the heterotic string (the compact version).
Exceptional Lie groups |
E_{6} > E_{7} | E_{8} | F_{4} | G_{2} |