Abstract
The study of J-algebras in the previous chapter has yielded a description of all reduced J-algebras. In the present chapter we develop another description 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 end of Ch. 5, that every J-algebra over an algebraic number field is reduced (see Cor. 6.3.4).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Historical Notes
T.A. Springer: Oktaven, Jordan-Algebren und Ausnahmegruppen. Vorlesungsausarbeitung von P. Eysenbach. Mimeogr. notes, Math. Inst. Göttingen, 1963.
A.A. Albert: A construction of exceptional Jordan division algebras. Ann. of Math. 67 (1958), 1–28.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Springer, T.A., Veldkamp, F.D. (2000). Proper J-algebras and Twisted Composition Algebras. In: Octonions, Jordan Algebras and Exceptional Groups. Springer Monographs in Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-12622-6_6
Download citation
DOI: https://doi.org/10.1007/978-3-662-12622-6_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-08563-5
Online ISBN: 978-3-662-12622-6
eBook Packages: Springer Book Archive