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This representation captures the full information of the index except when the underlying Dynkin diagram is D 4 , in which case one must distinguish between an action by the cyclic group C 3 or the permutation group S 3. Special fields : Exists over the reals and number fields; does not exist over finite fields or a p -adic field. Alternatively, an index can be represented using the name of the underlying Dykin diagram together with additional superscripts and subscripts, to be explained momentarily. A group of type G 2 is always the automorphism group of an octonion algebra [2]. Special fields : Exists over a finite field, the reals, a p -adic field, and a number field. The possible irreducible indices were classified by Jacques Tits [1] , and this classification is reproduced below.

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Algebraic group : If k has characteristic 2, the same as for C n except that h is a hermitian form of discriminant 1 and index r.

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Algebraic Group : The automorphism group of an exceptional simple Jordan algebra J containing nonzero nilpotent elements, no two of which are nonproportional and orthogonal. Categories : Algebraic groups Mathematics-related lists. Algebraic Group : The automorphism group of an exceptional simple Jordan algebra J containing nonproportional orthogonal nilpotent elements.

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