Geodesic
Octonion Algebras over Rings Are Not Determined by their Norms
Canadian mathematical bulletin, Tome 57 (2014) no. 2, pp. 303-309

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

Answering a question of H. Petersson, we provide a class of examples of a pair of octonion algebras over a ring having isometric norms.
DOI : 10.4153/CMB-2012-044-7
Mots-clés : 14L24, 20G41, Octonion algebras, torsors, descent 
Gille, Philippe. Octonion Algebras over Rings Are Not Determined by their Norms. Canadian mathematical bulletin, Tome 57 (2014) no. 2, pp. 303-309. doi: 10.4153/CMB-2012-044-7
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[1] [1] Bix, R., Isomorphism theorems for octonion planes over local rings. Trans. Amer. Math. Soc. 266 (1981, no. 2, 423–439. Google Scholar | DOI

[2] [2] Colliot–Théléne, J.-L. and Sansuc, J.-J., Fibrés quadratiques et composantes connexes réelles. Math. Ann. 244 (1979, 105–134. Google Scholar | DOI

[3] [3] Demazure, M. and Gabriel, P., Groupes algébriques. North-Holland, Amsterdam, 1970. Google Scholar

[4] [4] Giraud, J., Cohomologie non-abélienne. Die Grundlehren der mathematischenWissenschaften, 179, Springer-Verlag, Berlin-New York, 1971. Google Scholar

[5] [5] Igusa, J.-I., A classification of spinors up to dimension twelve. Amer. J. Math. 92 (1970, 997–1028. Google Scholar | DOI

[6] [6] Knus, M.-A., Quadratic and hermitian forms over rings. Grundlehren der mathematischen Wissenschaften, 294, Springer-Verlag, Berlin, 1991. Google Scholar

[7] [7] Knus, M.-A., Ojanguren, M., and Sridharan, R., Quadratic forms and Azumaya algebras. J. Reine Angew. Math. 303/304 (1978, 231–248. Google Scholar

[8] [8] Loos, O., Petersson, H. P, and Racine, M. L., Inner derivations of alternative algebras over commutative rings. Algebra Number Theory 2 (2008, no. 8, 927–968. Google Scholar | DOI

[9] [9] Mimura, M., Homotopy theory of Lie groups. In: Handbook of algebraic topology, North-Holland, Amsterdam, 1995, pp. 951–991. Google Scholar | DOI

[10] [10] Petersson, H. P., Composition algebras over algebraic curves of genus zero. Trans. Amer. Math. Soc. 337 (1993, no. 1, 473–493. Google Scholar | DOI

[11] [11] Séminaire de Géométrie algébrique de l’I.H.E.S., 1963-1964, schémas en groupes. dirigé par M. Demazure et A. Grothendieck, Lecture Notes in Mathematics, 151–153. Springer-Verlag, Berlin, 1970. Google Scholar

[12] [12] Springer, T. A. and Veldkamp, F. D., Octonions, Jordan algebras and exceptional groups. Springer Monographs in Mathematics, Springer-Verlag, Berlin, 2000. Google Scholar

[13] [13] Steinmetz-Zikesch, A., Algèbres de Lie de dimension infinie et théorie de la descente. Mém. Soc. Math. Fr., to appear. Google Scholar

[14] [14] van der Blij, F. and Springer, T. A., The arithmetics of octaves and of the group G2. Nederl. Akad. Wetensch. Proc. Ser. A 62 = Indag. Math. 21 (1959, 406–418. Google Scholar

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