|
This article is cited in 11 scientific papers (total in 11 papers)
Division algebras with the same maximal subfields
V. I. Chernousova, A. S. Rapinchukb, I. A. Rapinchukc 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.
Received: 09.09.2014
Citation:
V. I. Chernousov, A. S. Rapinchuk, I. A. Rapinchuk, “Division algebras with the same maximal subfields”, Uspekhi Mat. Nauk, 70:1(421) (2015), 89–122; Russian Math. Surveys, 70:1 (2015), 83–112
Linking options:
https://www.mathnet.ru/eng/rm9649https://doi.org/10.1070/RM2015v070n01ABEH004937 https://www.mathnet.ru/eng/rm/v70/i1/p89
|
Statistics & downloads: |
Abstract page: | 536 | Russian version PDF: | 208 | English version PDF: | 15 | References: | 56 | First page: | 30 |
|