Abstract
In this chapter we deal with algebraic triality in the group of similarities and in the orthogonal group O(N) of the norm N of an octonion algebra C,and with the related triality in the Lie algebras of these groups, usually called local triality. Geometric triality on the quadric N(x) = 0 in case N 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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Historical Notes
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E. Cartan: Le principe de dualité et la théorie des groupes simples et semi-simples. Bull. Sci. Math. 49 (1925), 361–374. OEuvres 1, 1, 555–568.
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N. Jacobson: Exceptional Lie Algebras. Lecture Notes in Pure and Applied Mathematics, Vol. 1. Marcel Dekker, New York, 1971.
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© 2000 Springer-Verlag Berlin Heidelberg
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Springer, T.A., Veldkamp, F.D. (2000). Triality. In: Octonions, Jordan Algebras and Exceptional Groups. Springer Monographs in Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-12622-6_3
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DOI: https://doi.org/10.1007/978-3-662-12622-6_3
Publisher Name: Springer, Berlin, Heidelberg
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