Generators of Automorphism Groups of Cayley Algebras

  • Huberta Lausch
Part of the NATO ASI Series book series (ASIC, volume 333)


All involutory automorphisms of a Cayley algebra C form a generating set for the automorphism group of C. The minimal number of involutory automorphisms needed to express an automorphism of C is called its length. For Cayley algebras C over fields of characteristic not 2 we determine the length of any automorphism of C. It turns out that every automorphism of a Cayley algebra is the product of at most three involutory automorphisms. Hence the automorphism groups of Cayley algebras are trireflectional. We derive some criteria for the bireflectionality of the automorphism group of a Cayley algebra and present examples of bi- and of trireflectional automorphism groups. Some remarks on Cayley algebras over fields of characteristic 2 are added.


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Copyright information

© Springer Science+Business Media Dordrecht 1991

Authors and Affiliations

  • Huberta Lausch
    • 1
  1. 1.Department of MathematicsUniversity of WürzburgWürzburgWest-Germany

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