Titlebook: Octonions, Jordan Algebras and Exceptional Groups; Tonny A. Springer,Ferdinand D. Veldkamp Book 2000 Springer-Verlag Berlin Heidelberg 200

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Triality,nd with the related triality in the Lie algebras of these groups, usually called local triality. Geometric triality on the quadric .(.) = 0 in case . is isotropic will be left aside; the reader interested in the subject may consult [B1Sp 60] and [Che 54, Ch. IV].

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J-algebras and Albert Algebras, algebras. Our interest in Albert algebras is motivated by their connections with exceptional simple algebraic groups of type E. and F., a topic we will deal with in Ch. 7. They also play a role in a description of algebraic groups of type E. and E., but we leave that aspect aside. We will not enter

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Proper J-algebras and Twisted Composition Algebras,tion of J-algebras which includes all nonreduced ones. For this purpose we make a link between J-algebras and twisted composition algebras. We will see that a J-algebra is reduced if and only if certain twisted composition algebras are reduced. This will lead to the result, already announced at the

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https://doi.org/10.1007/978-3-662-12622-6Albert Algebras; Algebraic structure; Exceptional Groups; Octonions; algebra

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The Automorphism Group of an Octonion Algebra,In this chapter we study the group . = Aut(.) of automorphisms of an octonion algebra . over a field .. By “automorphism” we will in this chapter always understand a .. Since automorphisms leave the norm invariant, Aut(.) is a subgroup of the orthogonal group O(.) of the norm of ..

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Tonny A. Springer,Ferdinand D. VeldkampIncludes supplementary material: