On chains in division algebras of degree 3

Darrell Haile; Jung-Miao Kuo; Jean-Pierre Tignol

doi:10.1016/j.crma.2009.06.007

Algebra

On chains in division algebras of degree 3

Presented by: Jean-Pierre Serre

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

Comptes Rendus. Mathématique, Volume 347 (2009) no. 15-16, pp. 849-852

Abstract (Original language)
Résumé

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: 2009-06-02
Accepted: 2009-06-11
Published online: 2009-07-03

DOI: 10.1016/j.crma.2009.06.007

Author's affiliations:

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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     title = {On chains in division algebras of degree 3},
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     doi = {10.1016/j.crma.2009.06.007},
     language = {en},
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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

References
Cited by

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[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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