Geodesic
Simple Algebras that Generalize the Jordan Algebra M3 8
Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 282-290

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper we discuss a generalization of the split exceptional Jordan algebra M3 8() of the 3 X 3 hermitian matrices with elements in the split Cayley-Dickson algebra (1). The generalization consists of replacing by the non-commutative Jordan algebra ≡ (A, ƒ, s, t) discussed in (2; 3) and forming the set of 3 X 3 hermitian matrices M3 m() ≡ M with elements in the m-dimensional algebra . With the usual definition of multiplication X · Y = 1⁄2(XY + YX), M becomes a commutative algebra and we have the following theorem, which shows how the structure of M is reflected by that of . 
Sagle, Arthur A. Simple Algebras that Generalize the Jordan Algebra M3 8. Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 282-290. doi: 10.4153/CJM-1966-030-7
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[1] 1. Paige, L. J., Jordan algebras, Studies in Modern Algebra, vol. 2 (Amer. Math. Soc, 1963). Google Scholar

[2] 2. Paige, L. J., A note on noncommutative Jordan algebras, Portugal. Math., 16 (1957), 15–18. Google Scholar

[3] 3. Sagle, A., On anti-commutative algebras with an invariant form, Can. J. Math., 16 (1964), 370–378. Google Scholar

[4] 4. van der Waerden, B. L., Modern algebra, vol. II (New York, 1950). Google Scholar

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