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In page Adjoint representation:
"The upper-case/lower-case notation is used extensively in the literature. Thus, for example, a vector x in the algebra generates a vector field X in the group G. Similarly, the adjoint map adxy = [x,y] of vectors in is homomorphic[clarification needed] to the Lie derivative LXY = [X,Y] of vector fields on the group G considered as a manifold.
