Formulae for the levels and sublevels of certain quaternion and octonion algebras are established. Corollaries concerning the equality of levels and sublevels of quaternion algebras with those of associated octonion algebras are presented.
On étudie les sommes de carrés dans certaines algèbres de quaternions et dʼoctonions et on établit des formules pour leurs niveaux et sous-niveaux. On en déduit des corollaires sur lʼégalité des niveaux et sous-niveaux des algèbres de quaternions et de ceux dʼalgèbres dʼoctonions associées.
Accepted:
Published online:
James OʼShea 1, 2
@article{CRMATH_2011__349_5-6_239_0, author = {James O'Shea}, title = {Sums of squares in certain quaternion and octonion algebras}, journal = {Comptes Rendus. Math\'ematique}, pages = {239--242}, publisher = {Elsevier}, volume = {349}, number = {5-6}, year = {2011}, doi = {10.1016/j.crma.2011.01.022}, language = {en}, }
James OʼShea. Sums of squares in certain quaternion and octonion algebras. Comptes Rendus. Mathématique, Volume 349 (2011) no. 5-6, pp. 239-242. doi : 10.1016/j.crma.2011.01.022. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.01.022/
[1] Levels of quaternion algebras, Archiv der Mathematik, Volume 90 (2008) no. 5, pp. 401-411
[2] Levels and sublevels of quaternion algebras, Mathematical Proceedings of the Royal Irish Academy A, Volume 110 (2010) no. 1, pp. 95-98
[3] Introduction to Quadratic Forms over Fields, American Mathematical Society, 2005
[4] Bounds on the levels of composition algebras, Mathematical Proceedings of the Royal Irish Academy A, Volume 110 (2010) no. 1, pp. 21-30
[5] Représentation de −1 comme somme de carrés dans certaines algèbres de quaternions, C. R. Acad. Sci. Paris, Ser. I, Volume 305 (1987) no. 13, pp. 583-586
Cited by Sources:
Comments - Policy