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Over an algebraically closed field, this is the only form; however, over other fields, there are often many other forms, or "twists" of E 8, which are classified in the general framework of Galois cohomology (over a perfect field k) by the set H 1 (k,Aut(E 8)), which, because the Dynkin diagram of E 8 (see below) has no automorphisms, coincides ...