Algebra
On the genus of a division algebra
Comptes Rendus. Mathématique, Volume 350 (2012) no. 17-18, pp. 807-812.

We define the genus gen(D) of a finite-dimensional central division algebra D over a field K as the set of all classes [D] in the Brauer group Br(K) that are represented by central division K-algebras D having the same maximal subfields as D. We give examples where gen(D) is reduced to a single element, and other examples where it is finite.

Nous définissons le genre gen(D) dʼun corps gauche central D de dimension finie sur un corps K comme lʼensemble des classes [D] dans le groupe de Brauer Br(K) qui sont représentées par des corps gauches D de centre K ayant les mêmes sous-corps maximaux que D. Nous donnons des exemples où gen(D) est réduit à un seul élément, ainsi que dʼautres où gen(D) est fini.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2012.09.014
Chernousov, Vladimir I. 1; Rapinchuk, Andrei S. 2; Rapinchuk, Igor A. 3

1 Department of Mathematics, University of Alberta, Edmonton, Alberta T6G 2G1, Canada
2 Department of Mathematics, University of Virginia, Charlottesville, VA 22904-4137, USA
3 Department of Mathematics, Yale University, New Haven, CT 06520-8283, USA
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Chernousov, Vladimir I.; Rapinchuk, Andrei S.; Rapinchuk, Igor A. On the genus of a division algebra. Comptes Rendus. Mathématique, Volume 350 (2012) no. 17-18, pp. 807-812. doi : 10.1016/j.crma.2012.09.014. http://www.numdam.org/articles/10.1016/j.crma.2012.09.014/

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