ALGEBRAIC GROUPS OF TYPE D-4, TRIALITY, AND COMPOSITION ALGEBRAS

作者：Chernousov Vladimir^*; Elduque Alberto; Knus Max Albert; Tignol Jean Pierre

来源：Documenta Mathematica, 2013, 18: 413-468.

DOI：10.4171/dm/405

• Algebraic group of type D-4
• triality
• outer automorphism of order 3
• composition algebra
• symmetric composition
• octonions
• Okubo algebra

Conjugacy classes of outer automorphisms of order 3 of simple algebraic groups of classical type D-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 G(2); for the other type they are simple of type A(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.

• 出版日期2013