Download this article
Download this article For screen
For printing
Recent Issues
Volume 18
Volume 16
Volume 15
Volume 14
Volume 13
Volume 12
Volume 11
Volume 10
Volume 9
Volume 8
Volume 6+7
Volume 5
Volume 4
Volume 3
Volume 2
Volume 1
The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN (electronic): 2640-7345
ISSN (print): 2640-7337
Author Index
To Appear
 
Other MSP Journals
This article is available for purchase or by subscription. See below.
Incidence geometry of the Fano plane and Freudenthal's ansatz for the construction of octonions and split octonions

Michel Rausch de Traubenberg and Marcus Slupinski

Vol. 19 (2022), No. 4, 165–181
Abstract

We consider structures on a Fano plane which allow a generalisation of Freudenthal’s construction of a norm and a bilinear multiplication law on an eight-dimensional vector space 𝕆 canonically associated to . We first determine necessary and sufficient conditions in terms of the incidence geometry of for these structures to give rise to division composition algebras, and classify the corresponding structures using a logarithmic version of the multiplication. We then show how these results can be used to deduce analogous results in the split composition algebra case.

PDF Access Denied

We have not been able to recognize your IP address 3.236.143.154 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

Keywords
Fano plane, incidence geometry, octonions
Mathematical Subject Classification
Primary: 17Dxx, 51Axx, 51Exx
Milestones
Received: 25 February 2022
Revised: 26 July 2022
Accepted: 25 August 2022
Published: 1 December 2022
Authors
Michel Rausch de Traubenberg
IPHC
University of Strasbourg
Strasbourg
France
Marcus Slupinski
Institut de recherche mathématique avancée
CNRS
Strasbourg
France