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Adams, J.F. (1958). On the nonexistence of elements of Hopf invariant one. Bull. Amer. Math. Soc., 64, 279–282.

Baez, J.C. (2002). The octonions. Bull. Amer. Math. Soc. (N.S.), 39(2), 145–205.

Borel, A., Serre, J.-P. (1953). Groupes de Lie et puissances réduites de Steenrod. Amer. J. Math., 75, 409–448.

Bott, R., Milnor, J. (1958). On the parallelizability of the spheres. Bull. Amer. Math. Soc., 64, 87–89.

Cartan, E. (1925). Le principe de dualité et la théorie des groupes simples et semi-simples. Bull. Sci. Math., 49, 361–374.

Chernousov, V., Elduque, A., Knus, M.-A., Tignol, J.-P. (2013). Algebraic groups of type D₄, triality, and composition algebras. Doc. Math., 18, 413–468.

Conway, J.H., Smith, D.A. (2003). On Quaternions and Octonions: Their Geometry, Arithmetic, and Symmetry. A K Peters, Ltd., Natick.

Cunha, I., Elduque, A. (2007). An extended Freudenthal magic square in characteristic 3. J. Algebra, 317(2), 471–509.

Ebbinghaus, H.-D., Hermes, H., Hirzebruch, F., Koecher, M., Mainzer, K., Neukirch, J., Prestel, A., Remmert, R. (1991). Numbers, Ewing, J.H. (ed.). With an introduction by Lamotke, K. Translated by Orde, H.L.S. Springer-Verlag, New York.

Elduque, A. (1997). Symmetric composition algebras. J. Algebra, 196(1), 282–300.

Elduque, A. (2004). The magic square and symmetric compositions. Rev. Mat. Iberoamericana, 20(2), 475–491.

Elduque, A., Myung, H.C. (1990). On Okubo algebras. In From Symmetries to Strings: Forty Years of Rochester Conferences, Das, E. (ed.). World Science Publishing, River Edge, 299–310.

Elduque, A., Myung, H.C. (1991). Flexible composition algebras and Okubo algebras. Comm. Algebra, 19(4), 1197–1227.

Elduque, A., Myung, H.C. (1993). On flexible composition algebras. Comm. Algebra, 21(7), 2481–2505.

Elduque, A., Pérez, J.M. (1996). Composition algebras with associative bilinear form. Comm. Algebra, 24(3), 1091–1116.

Elduque, A., Pérez, J.M. (1997). Infinite-dimensional quadratic forms admitting composition. Proc. Amer. Math. Soc., 125(8), 2207–2216.

Elman, R., Karpenko, N., Merkurjev, A. (2008). The Algebraic and Geometric Theory of Quadratic Forms. American Mathematical Society, Providence.

Faulkner, J.R. (1988). Finding octonion algebras in associative algebras. Proc. Amer. Math. Soc., 104(4), 1027–1030.

Frobenius, F.G. (1878). Über lineare substitutionen und bilineare formen. J. Reine Angew. Math., 84, 1–63.

Gille, P. (2014). Octonion algebras over rings are not determined by their norms. Canad. Math. Bull., 57(2), 303–309.

Hurwitz, A. (1898). Über die komposition der quadratischen formen von beliebig vielen variablen. Nachr. Ges. Wiss. Göttingen, 309–316.

Jacobson, N. (1958). Composition algebras and their automorphisms. Rend. Circ. Mat. Palermo, 7(2), 55–80.

Kaplansky, I. (1953). Infinite-dimensional quadratic forms admitting composition. Proc. Amer. Math. Soc., 4, 956–960.

Kervaire, M.A. (1958). Non-parallelizability of the n-sphere for n > 7. Proc. Natl. Acad. Sci. 44(3), 280–283.

Knus, M.-A., Merkurjev, A., Rost, M., Tignol, J.-P. (1998). The Book of Involutions. With a preface in French by J. Tits. American Mathematical Society, Providence.

Okubo, S. (1978). Pseudo-quaternion and pseudo-octonion algebras. Hadronic J., 1(4), 1250–1278.

Okubo, S. (1995). Introduction to Octonion and Other Non-associative Algebras in Physics. Cambridge University Press, Cambridge.

Okubo, S., Osborn, J.M. (1981a). Algebras with nondegenerate associative symmetric bilinear forms permitting composition. Comm. Algebra, 9(12), 1233–1261.

Okubo, S., Osborn, J.M. (1981b). Algebras with nondegenerate associative symmetric bilinear forms permitting composition II. Comm. Algebra, 9(20), 2015–2073.

Petersson, H.P. (1969). Eine Identität fünften Grades, der gewisse Isotope von Kompositions-Algebren genügen. Math. Z., 109, 217–238.

Petersson, H.P. (2005). Letter to the editor: An observation on real division algebras. European Math. Soc. Newsletter, 57, 20.

Rodrigues, O. (1840). Des lois géométriques qui régissent les déplacements d’un système solide dans l’espace, et de la variation des coordonnées provenant de ces déplacements considérés indépendamment des causes qui peuvent les produire. J. de Mathématiques Pures et Appliquées, 5, 380–440.

Rodríguez-Palacios, A. (2004). Absolute-valued Algebras, and Absolute-valuable Banach Spaces, Advanced Courses of Mathematical Analysis. World Science Publishing, Hackensack.

Shapiro, D.B. (2000). Compositions of Quadratic Forms. Walter de Gruyter & Co., Berlin.

Springer, T.A., Veldkamp, F.D. (2000). Octonions, Jordan Algebras and Exceptional Groups. Springer Monographs in Mathematics, Springer-Verlag, Berlin.

Study, E. (1913). Grundlagen und ziele der analytischer kinematik. Sitz. Ber. Berliner Math. Gesellschaft, 12, 36–60.

Tits, J. (1959). Sur la trialité et certains groupes qui s’en déduisent. Inst. Hautes Études Sci. Publ. Math., 2, 13–60.

Urbanik, K., Wright, F.B. (1960). Absolute-valued algebras. Proc. Amer. Math. Soc., 11, 861–866.

van der Blij, F., Springer, T.A. (1959). The arithmetics of octaves and of the group G₂. Nederl. Akad. Wetensch. Proc. Ser. A 62 = Indag. Math., 21, 406–418.

Zorn, M. (1933). Alternativkörper und quadratische systeme. Abh. Math. Sem. Univ. Hamburg, 9(1), 395–402.

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