G can be written as g = exp(i c_i λ_i ), where c_i are numbers and λ_i are group generators. The generators are in an algebra, because
you can add and multiply them, while the group elements are in a group, because you can only multiply them. For example, the real numbers form an algebra, but rotations are a group.
Lie groups are a class of groups, including the Lorentz group, with an infinite number of elements but a finite number of generators. The generators of the Lie group form an algebra called its Lie algebra.
FORRESTEN: Enten har jeg løpt et feynmandiagram, eller et hjerte