By expanding the group elements written in the canonical exponential form about the origin, derive the Lie algebra (left[X_{a}, X_{b} ight]=i f_{a b c} X_{c}).

By expanding the group elements written in the canonical exponential form about the origin, derive the Lie algebra \(\left[X_{a}, X_{b}\right]=i f_{a b c} X_{c}\). A commutator can be defined by taking the difference between the product of two group elements and the product in reverse order.