V. I. Chernousov, A. S. Rapinchuk, I. A. Rapinchuk, “Division algebras with the same maximal subfields”, Uspekhi Mat. Nauk, 2015, Volume 70, Issue 1(421),Pages <nobr>89

This article is cited in 11 papers

Division algebras with the same maximal subfields

V. I. Chernousov^a, A. S. Rapinchuk^b, I. A. Rapinchuk^c

^a University of Alberta, Edmonton, Canada
^b University of Virginia, Charlottesville, USA
^c Harvard University, Cambridge, USA

Abstract: This is a survey of recent results related to the problem of characterizing finite-dimensional division algebras by the set of isomorphism classes of their maximal subfields. Also discussed are various generalizations of this problem and some of its applications. In the last section the problem is extended to the context of absolutely almost simple algebraic groups.
Bibliography: 51 titles.

Keywords: division algebra, unramified Brauer group, semisimple algebraic groups.

UDC: 512.552

MSC: 11R52, 12E15, 20G15

Received: 09.09.2014

DOI: 10.4213/rm9649