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Hello! I am reading some representation theory/Lie algebra stuff and at a point the author says "the states of the adjoint representation correspond to generators". I am not sure I understand this. I thought that the states of a representation are the vectors in the vector space on which the representation acts. So for a 3D representation of SO(3), the states would be euclidian vectors. But in this case, the generators are forming the matrices that act on a given vector space (in the case of SO(3) they would be the ##L_x## matrices). So how can the generators, be also states of a representation, when they generate the representation? I assume I miss understood something, so I would really appreciate if someone can clarify this for me, or point me towards a good reading. Thank you!