Books on the Octonions:

  1. Geoffrey M. Dixon, Division Algebras: Octonions, Quaternions, Complex Numbers and the Algebraic Design of Physics, Kluwer Academic Publishers, Boston, 1994.

  2. Feza Gürsey and Chia-Hsiung Tze, On the Role of Division, Jordan, and Related Algebras in Particle Physics, World Scientific, Singapore, 1996.

  3. S. Okubo, Introduction to Octonion and Other Non-Associative Algebras in Physics, Cambridge University Press, Cambridge, 1995.

    Other related books:

  4. Clifford Algebras with Numeric and Symbolic Computations, eds. Rafa\l Ab\l amowicz, Pertti Lounesto, Josep M. Parra, Birkhäuser, Boston, 1996.

  5. Stephen L. Adler, Quaternionic Quantum Mechanics and Quantum Fields, Oxford University Press, New York, 1995.

  6. Emil Artin, Geometric Algebra, John Wiley & Sons, New York, 1957 & 1988.

  7. William E. Baylis, Electrodynamics: a Modern Geometrical Approach, Birkhäuser Boston, Cambridge, 1999.

  8. Michael J. Crowe, A History of Vector Analysis, Dover, Mineola, NY, 1984 (originally published 1967).

  9. M. B. Green, J. H. Schwarz, and E. Witten, Superstring Theory, Cambridge University Press, Cambridge, 1987.

  10. F. Reese Harvey, Spinors and Calibrations, Academic Press, Boston, 1990.

  11. Nathan Jacobson, Structure and Representations of Jordan Algebras, Amer.  Math.  Soc. Colloq. Publ. 39, American Mathematical Society, Providence, 1968.

  12. P. Lounesto, Clifford Algebras and Spinors, Cambridge University Press, Cambridge, 1997.

  13. Roger Penrose and Wolfgang Rindler, Spinors and Space-Time, Cambridge University Press, Cambridge, 1984 & 1986.

  14. Boris Rosenfeld, Geometry of Lie Groups, Kluwer, Dordrecht, 1997.

  15. Richard D. Schafer, An Introduction to Nonassociative Algebras, Academic Press, New York, 1966 & Dover, Mineola NY, 1995.

    Papers by our group:

  16. David B. Fairlie and Corinne A. Manogue, Lorentz Invariance and the Composite String, Phys. Rev. D34, 1832–1834 (1986).

  17. David B. Fairlie and Corinne A. Manogue, A Parameterization of the Covariant Superstring, Phys. Rev. D36, 475–479 (1987).

  18. Corinne A. Manogue and Anthony Sudbery, General Solutions of Covariant Superstring Equations of Motion, Phys. Rev. D40, 4073–4077 (1989).

  19. Corinne A. Manogue and Jörg Schray, Finite Lorentz transformations, automorphisms, and division algebras, J. Math. Phys. 34, 3746–3767 (1993).

  20. Jörg Schray, Octonions and Supersymmetry, Ph.D. thesis, Department of Physics, Oregon State University, 1994.

  21. Jörg Schray, The General Classical Solution of the Superparticle, Class. Quant. Grav. 13, 27 (1996).

  22. Jörg Schray & Corinne A. Manogue, Octonionic Representations of Clifford Algebras and Triality, Foundations of Physics, 26 17–70 (1996).

  23. Tevian Dray and Corinne A. Manogue, The Octonionic Eigenvalue Problem, Adv. Appl. Clifford Algebras 8, 341–364 (1998).

  24. Tevian Dray and Corinne A. Manogue, Finding Octonionic Eigenvectors Using {\slshape Mathematica}, Comput. Phys. Comm. 115, 536–547 (1998).

  25. Corinne A. Manogue and Tevian Dray, Dimensional Reduction, Mod. Phys. Lett. A14, 93–97 (1999).

  26. Corinne A. Manogue and Tevian Dray, Octonionic Möbius Transformations, Mod. Phys. Lett. A14, 1243–1255 (1999).

  27. Tevian Dray and Corinne A Manogue The Exceptional Jordan Eigenvalue Problem, Internat. J. Theoret. Phys. 38, 2901–2916 (1999).

  28. Tevian Dray and Corinne A. Manogue, Quaternionic Spin, in Clifford Algebras and their Applications in Mathematical Physics, eds. Rafa\l  Ab\l amowicz and Bertfried Fauser, Birkhäuser, Boston, 2000, pp. 29–46.

  29. Tevian Dray, Jason Janesky, and Corinne A. Manogue, Octonionic Hermitian Matrices with Non-Real Eigenvalues Adv. Appl. Clifford Algebras 10, 193–216 (2000).

  30. Tevian Dray, Jason Janesky, and Corinne A. Manogue, Some Properties of $3\times3$ Octonionic Hermitian Matrices with Non-Real Eigenvalues, Oregon State University, 2000, 12 pages.

  31. Tevian Dray, Corinne A. Manogue, and Susumu Okubo, Orthonormal Eigenbases over the Octonions, Algebras Groups Geom. (to appear).

    Other related papers:

  32. A. Adrian Albert, On a Certain Algebra of Quantum Mechanics, Ann. Math. 35, 65–73 (1934).

  33. Claude Chevalley and R. D. Schafer, The Exceptional Simple Lie Algebras $F_4$ and $E_6$, Proc. Nat. Acad. Sci. U.S.A. 36, 137–141 (1950).

  34. K. W. Chung and A. Sudbery, Octonions and the Lorentz and Conformal Groups of Ten-Dimensional Space-Time, Phys. Lett. B198, 161 (1987).

  35. L. E. Dickson, Ann. Math. 20, 155 (1919).

  36. P. A. M. Dirac, Proc. Roy. Irish Acad., Sect. A, Vol. L, 261 (1945).

  37. Freeman J. Dyson, Quaternion Determinants, Helv. Phys. Acta 45, 289–302 (1972).

  38. Hans Freudenthal, Oktaven, Ausnahmegruppen, und Oktavengeometrie, Mathematisch Instituut der Rijksuniversiteit te Utrecht, 1951 (mimeographed); new revised edition, 1960; reprinted as Geom. Dedicata 19, 1–63 (1985).

  39. Hans Freudenthal, Zur Ebenen Oktavengeometrie, Proc. Kon. Ned. Akad. Wet. A56, 195–200 (1953).

  40. Hans Freudenthal, Lie Groups in the Foundations of Geometry, Adv. Math. 1, 145–190 (1964).

  41. H. H. Goldstine & L. P. Horwitz, On a Hilbert Space with Nonassociative Scalars, Proc. Nat. Aca. 48, 1134 (1962).

  42. P. Jordan, Über die Multiplikation quantenmechanischer Größen, Z. Phys. 80, 285–291 (1933).

  43. P. Jordan, J. von Neumann, and E. Wigner, On an Algebraic Generalization of the Quantum Mechanical Formalism, Ann. Math. 35, 29–64 (1934).

  44. T. Kugo and P. Townsend, Supersymmetry and the division algebras, Nucl. Phys. B221, 357 (1983).

  45. О. В. Огиевецкий, Характеристическое Урабнение для Матриц $3\times3$ над Октавами, Uspekhi Mat. Nauk 36, 197–198 (1981); translated in: O. V. Ogievetskii, The Characteristic Equation for $3\times3$ Matrices over Octaves, Russian Math. Surveys 36, 189–190 (1981).

  46. Susumu Okubo, Eigenvalue Problem for Symmetric $3\times3$ Octonionic Matrix, Adv. Appl. Clifford Algebras 9, 131–176 (1999).

  47. A. Sudbery, J. Phys. A17, 939 (1984).