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Octonions and triality

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Bibliography

  • Adams J. F., On the non-existence of elements of Hopf invariant one.Ann. of Math. 72 (1960), 20–104.

    Article  MathSciNet  Google Scholar 

  • Adams J. F., Vector fields of spheres.Ann. of Math. 75 (1962), 603–632.

    Article  MathSciNet  Google Scholar 

  • van der Blij F., History of the octaves.Simon Stevin 34 (1961), 106–125.

    MATH  MathSciNet  Google Scholar 

  • Cayley A., On Jacobi’s elliptic functions, in reply to Rev. Brice Bronwin and on quaternions.Phil. Mag. (3)26 (1845), 208–211.

    Google Scholar 

  • C. Chevalley C.,The Algebraic Theory of Spinors. Columbia University Press, New York, 1954.The Algebraic Theory of Spinors and Clifford Algebras. Springer, Berlin, 1997.

    Google Scholar 

  • Dixon G. M.,Division Algebras: Octonions, Quaternions, Complex Numbers and the Algebraic Design of Physics. Kluwer, Dordrecht, 1994.

    MATH  Google Scholar 

  • Ebbinghaus H.-D. et al. (eds.), “Numbers”, Springer, New York, 1991.

    MATH  Google Scholar 

  • Hahn A. J., Cayley algebras and the automorphisms ofPO ′8 (V) andPΩ ′8 (V).Amer. J. Math. 98 (1976), 953–987.

    Article  MATH  MathSciNet  Google Scholar 

  • Hahn A. J., Cayley algebras and the isomorphisms of the orthogonal over arithmetic and local domains.J. Algebra 45 (1977), 210–246.

    Article  MATH  MathSciNet  Google Scholar 

  • Harvey F. R.,Spinors and Calibrations. Academic Press, San Diego, 1990.

    MATH  Google Scholar 

  • Knus M.-A., A. Merkurjev, M. Rost, J.-P. Tignol:The Book of Involutions. American Mathematical Society, Colloquium Publications44, 1998.

  • Massey W. S., Cross products of vectors in higher dimensional Euclidean spaces.Amer. Math. Monthly 90 (1983), #10, 697–701.

    Article  MATH  MathSciNet  Google Scholar 

  • Micali A., Ph. Revoy:Modules quadratiques. Cahiers Mathématiques10, Montpellier, 1977.Bull. Soc. Math. France 63, suppl. (1979), 5–144.

  • Okubo S.,Octonions and Non-associative Algebras in Physics. Cambridge University Press, Cambridge, 1994.

    Google Scholar 

  • Porteous I. R.,Clifford Algebras and the Classical Groups. Cambridge University Press, Cambridge, 1995.

    MATH  Google Scholar 

  • Schafer R. D. On the algebras formed by the Cayley-Dickson process.Amer. J. Math. 76 (1954), 435–446.

    Article  MATH  MathSciNet  Google Scholar 

  • Springer T. A., F. D. Veldkamp:Octonions, Jordan Algebras and Exceptional Groups. Springer, Berlin, 2000.

    MATH  Google Scholar 

  • Wene G. P., A construction relating Clifford algebras and Cayley-Dickson algebras.J. Math. Phys. 25 (1984), 2351–2353.

    Article  MATH  ADS  MathSciNet  Google Scholar 

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  1. Institute of Mathematics, Helsinki University of Technology, Helsinki

    Pertti Lounesto

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  1. Pertti Lounesto
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Lounesto, P. Octonions and triality. AACA 11, 191–213 (2001). https://doi.org/10.1007/BF03042312

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  • DOI: https://doi.org/10.1007/BF03042312

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