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The Freudenthal-Springer-Tits constructions of exceptional Jordan algebras


Author: Kevin McCrimmon
Journal: Trans. Amer. Math. Soc. 139 (1969), 495-510
MSC: Primary 17.40
DOI: https://doi.org/10.1090/S0002-9947-1969-0238916-9
MathSciNet review: 0238916
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  • [1] H. Braun and M. Koecher, Jordan Algebren, Springer-Verlag, Berlin, 1965. MR 0204470 (34:4310)
  • [2] H. Freudenthal, Beziehungen der $ {E_7}$ and $ {E_8}$ zur Oktavenebene. I, Nederl. Akad. Wetensch. Proc. Ser. A 57 (1954), 218-230. MR 0063358 (16:108b)
  • [3] -, Beziehungen der $ {E_7}$ und $ {E_8}$ zur Oktavenebene. VIII, Nederl. Akad. Wetensch. Proc. Ser. A 62 (1959), 447-465.
  • [4] N. Jacobson, Structure and representations of Jordan algebras, Amer. Math. Soc. Colloq. Publ., Vol. 39, Amer. Math. Soc., Providence, R. I., 1968. MR 0251099 (40:4330)
  • [5] K. McCrimmon, A general theory of Jordan rings, Proc. Nat. Acad. Sci. U.S.A. 56 (1966), 1072-1079. MR 0202783 (34:2643)
  • [6] -, Generically algebraic algebras, Trans. Amer. Math. Soc. 127 (1967), 527-551. MR 0210758 (35:1644)
  • [7] -, Norms and noncommutative Jordan algebras, Pacific J. Math. 15 (1965), 925-956. MR 0204477 (34:4317)
  • [8] T. A. Springer, Characterization of a class of cubic forms, Nederl. Akad. Wetensch. Proc. Ser. A 65 (1962), 259-265. MR 0138661 (25:2104)
  • [9] J. Tits, The complete unpublished works of J. Tits.

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DOI: https://doi.org/10.1090/S0002-9947-1969-0238916-9
Article copyright: © Copyright 1969 American Mathematical Society

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