Algebraic groups of type D4D_4, triality, and composition algebras.

  • Vladimir Chernousov

  • Alberto Elduque

  • Max-Albert Knus

Algebraic groups of type $D_4$, triality, and composition algebras. cover
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Conjugacy classes of outer automorphisms of order 3 of simple algebraic groups of classical type D4D_4 are classified over arbitrary fields. There are two main types of conjugacy classes. For one type the fixed algebraic groups are simple of type G2G_2; for the other type they are simple of type A2A_2 when the characteristic is different from 3 and are not smooth when the characteristic is 3. A large part of the paper is dedicated to the exceptional case of characteristic 3. A key ingredient of the classification of conjugacy classes of trialitarian automorphisms is the fact that the fixed groups are automorphism groups of certain composition algebras.

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Vladimir Chernousov, Alberto Elduque, Max-Albert Knus, Algebraic groups of type D4D_4, triality, and composition algebras.. Doc. Math. 18 (2013), pp. 413–468

DOI 10.4171/DM/405