E_8 in that sense is the Lie group E_8. A Lie group has an associated Lie algebra, which has an associated root system, which gives rise to a root lattice. Th

E_8 in that sense is the Lie group E_8. A Lie group has an associated Lie algebra, which has an associated root system, which gives rise to a root lattice. This E_8 is the root lattice. So yes they're very closely related though not the same object.