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Jan 6, 2010 at 18:14 comment added user717 Thanks! I think I just found another way (but your's might be better, I don't know): According to Skolem-Noether Aut(End_k(V)) = Inn(End_k(V)) and this is is the image of the adjoint representation of GL(V) which has kernel Z(GL(V)). With the inverse of the induced isomorphism (of algebraic groups, I hope) I also get into PGL(V).
Jan 6, 2010 at 17:38 history answered Ben Webster CC BY-SA 2.5