On the genus of a division algebra

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 el...

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Published inComptes rendus. Mathématique Vol. 350; no. 17-18; pp. 807 - 812
Main Authors Chernousov, Vladimir I., Rapinchuk, Andrei S., Rapinchuk, Igor A.
Format Journal Article
LanguageEnglish
Published Paris Elsevier SAS 01.09.2012
Elsevier
Subjects
Exact sciences and technology
General mathematics
General, history and biography
Mathematics
Sciences and techniques of general use
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Summary: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.
ISSN:1631-073X
1778-3569
1778-3569
DOI:10.1016/j.crma.2012.09.014