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

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Asymptomatic

刺激

Twisted Composition Algebras,heory comes from exceptional Jordan algebras and twisted algebraic groups of type D.. In particular, the notion of reduced twisted composition algebra comes from reduced Jordan algebras. We refer to Ch. 6 for the details.

Flavouring

Proper J-algebras and Twisted Composition Algebras,e 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 end of Ch. 5, that every J-algebra over an algebraic number field is reduced (see Cor. 6.3.4).

滲透

Desert

Book 2000sults from algebra. In the group-theoretical part use is made of some results from the theory of linear algebraic groups. The book will be useful to mathematicians interested in octonion algebras and Albert algebras, or in exceptional groups. It is suitable for use in a graduate course in algebra.

怒目而視

Vital-Signs

J-algebras and Albert Algebras, into the general theory of Jordan algebras, but use an ad hoc characterization of the algebras under consideration by simple axioms, which are somewhat reminiscent of those for composition algebras. We call these algebras J-algebras, since they are in fact a limited class of Jordan algebras; see Remark 5.1.7.

Oligarchy

1439-7382 ebraic groups. The book will be useful to mathematicians interested in octonion algebras and Albert algebras, or in exceptional groups. It is suitable for use in a graduate course in algebra.978-3-642-08563-5978-3-662-12622-6Series ISSN 1439-7382 Series E-ISSN 2196-9922

harangue

Composition Algebras,ras with quadratic norms, we need some fundamental parts of the theory of quadratic forms, which we therefore recall in the first section. It will be shown that the norm on a composition algebra already determines the algebra up to isomorphism. This leads to a more or less explicit determination of