Triality and Algebraic Groups of Type 3D4
We determine which simple algebraic groups of type
3D4 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.
M.-A. Knus < knus@math.ethz.ch >
J.-P. Tignol < jean-pierre.tignol@uclouvain.be >