I've started to study Lie groups recently and one thing seems confusing to me. If we have a 1-parameter group, what will be its Lie algebra?
As far as I understood, the number of generators of the group is the number of parameters, so 1-parameter group has only one generator X. So, I guess, the algebra of one generator will be $[X, X] = 0$ ? The idea of this seems a little confusing, because it's just trivial. Am I mistaken in some point?