Geodesic
Triality and algebraic groups of type $^3\mathsf D_4$
Documenta mathematica, Alexander S. Merkurjev's Sixtieth Birthday (2015), pp. 387-405.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

We determine which simple algebraic groups of type $^3\mathsf D$ over arbitrary fields of characteristic different from 2 admit outer automorphisms of order 3, and classify these automorphisms up to conjugation. The criterion is formulated in terms of a representation of the group by automorphisms of a trialitarian algebra: outer automorphisms of order 3 exist if and only if the algebra is the endomorphism algebra of an induced cyclic composition; their conjugacy classes are in one-to-one correspondence with isomorphism classes of symmetric compositions from which the induced cyclic composition stems.
Classification : 20G15, 11E72, 17A75
Keywords: algebraic group of outer type $^3\mathsf{D}_4$, triality, outer automorphism of order 3, composition algebra, symmetric composition, cyclic composition, octonions, Okubo algebra 
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     author = {Knus, Max-Albert and Tignol, Jean-Pierre},
     title = {Triality and algebraic groups of type $^3\mathsf D_4$},
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Knus, Max-Albert; Tignol, Jean-Pierre. Triality and algebraic groups of type $^3\mathsf D_4$. Documenta mathematica, Alexander S. Merkurjev's Sixtieth Birthday (2015), pp. 387-405. http://geodesic.mathdoc.fr/item/DOCMA_2015__S2__a10/