Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Blomer, Valentin / Cohen, Frederick R. / Droste, Manfred / Duzaar, Frank / Echterhoff, Siegfried / Frahm, Jan / Gordina, Maria / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna

IMPACT FACTOR 2018: 0.867

CiteScore 2018: 0.71

SCImago Journal Rank (SJR) 2018: 0.898
Source Normalized Impact per Paper (SNIP) 2018: 0.964

Mathematical Citation Quotient (MCQ) 2018: 0.71

See all formats and pricing
More options …
Volume 27, Issue 5


Autotopies and quasigroup identities: New aspects of non-associative division algebras

Erik Darpö / José Maria Pérez Izquierdo
Published Online: 2013-11-26 | DOI: https://doi.org/10.1515/forum-2012-0087


In this article, we explore new aspects in the classification of non-associative division algebras. By a detailed study of the representations of the Lie group of autotopies of real division algebras we show that, if the group of autotopies has a sufficiently rich structure, then the algebra is isotopic to one of the classical real division algebras. This turns out to be the case for large classes of real division algebras, including many that are defined by identities. In several cases, a classification up to isomorphism can be worked out from this information.

Keywords: Division algebra; quasigroup; isotopy; inversion; Hurwitz algebra

MSC: 17A35; 17A30; 18B40

About the article

Received: 2012-06-02

Revised: 2012-11-21

Published Online: 2013-11-26

Published in Print: 2015-09-01

Funding Source: Swedish Research Council

Award identifier / Grant number: 623-2009709

Funding Source: Spanish Ministerio de Ciencia e Innovación

Award identifier / Grant number: MTM2010-18370-C04-03

Citation Information: Forum Mathematicum, Volume 27, Issue 5, Pages 2691–2745, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/forum-2012-0087.

Export Citation

© 2015 by De Gruyter.Get Permission

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

Erik Darpö
Mediterranean Journal of Mathematics, 2018, Volume 15, Number 2

Comments (0)

Please log in or register to comment.
Log in