Comptes Rendus
Algebra
On chains in division algebras of degree 3
Comptes Rendus. Mathématique, Volume 347 (2009) no. 15-16, pp. 849-852.

Let D be a division algebra of degree 3 over a field containing a primitive cube root of unity. We give two proofs of a theorem of Rost asserting that any two Kummer elements in D can be connected by a chain of length 4.

Soit D un corps gauche de degré 3 sur un corps contenant une racine cubique de l'unité. Nous donnons deux démonstrations d'un théorème de Rost établissant que deux éléments de Kummer quelconques de D peuvent être joints par une chaine de longueur 4.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2009.06.007

Darrell Haile 1; Jung-Miao Kuo 2; Jean-Pierre Tignol 3

1 Department of Mathematics, Indiana University, Bloomington, IN 47401, USA
2 Department of Mathematics, National Taiwan University, Taipei, Taiwan
3 Université catholique de Louvain, chemin du cyclotron, 2, B-1348 Louvain-la-Neuve, Belgium
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Darrell Haile; Jung-Miao Kuo; Jean-Pierre Tignol. On chains in division algebras of degree 3. Comptes Rendus. Mathématique, Volume 347 (2009) no. 15-16, pp. 849-852. doi : 10.1016/j.crma.2009.06.007. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.06.007/

[1] F. van der Blij; T.A. Springer Octaves and triality, Nieuw Arch. Wisk. (3), Volume 8 (1960), pp. 158-169

[2] P.J. Cameron Projective and Polar Spaces, Queen Mary and Westfield Coll., London, 1991

[3] M.-A. Knus et al. The Book of Involutions, Amer. Math. Soc., Providence, RI, 1998

[4] M. Rost The chain lemma for Kummer elements of degree 3, C. R. Acad. Sci. Paris, Sér. I, Volume 328 (1999) no. 3, pp. 185-190

[5] J. Tits Buildings of Spherical Type and Finite BN Pairs, Lecture Notes in Mathematics, Springer-Verlag, New York, 1974

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