Transformation Groups

, Volume 14, Issue 2, pp 361–386 | Cite as

Trialitarian automorphisms of lie algebras

  • M.-A. Knus


Over an algebraically closed field of characteristic zero simple Lie algebras admit outer automorphisms of order 3 if and only if they are of type D4. Moreover, thereare two conjugacy classes of such automorphisms. Among orthogonal Lie algebras over arbitrary fields of characteristic zero, only orthogonal Lie algebras relative to quadratic norm forms of Cayley algebras admit outer automorphisms of order 3. We give a complete list of conjugacy classes of outer automorphisms of order 3 for orthogonal Lie algebras over arbitrary fields of characteristic zero. For the norm form of a given Cayley algebra, one class is associated with the Cayley algebra and the others with central simple algebras of degree 3 with involution of the second kind such that the cohomological invariant of the involution is the norm form.


Conjugacy Class Dynkin Diagram Algebraic Closure Outer Automorphism Central Simple Algebra 
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© Birkhäuser Boston 2008

Authors and Affiliations

  1. 1.ETH Zürich, Mathematik DepartementZürichSwitzerland

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