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
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.
An octonionic construction of $E_8$ and the Lie algebra magic square

Robert A. Wilson, Tevian Dray and Corinne A. Manogue

Vol. 20 (2023), No. 2-3, 611–634

We give a new construction of the Lie algebra of type E8, in terms of 3 × 3 matrices, such that the Lie bracket has a natural description as the matrix commutator. This leads to a new interpretation of the Freudenthal–Tits magic square of Lie algebras, acting on themselves by commutation.

Dedicated to the memory of Jacques Tits

PDF Access Denied

We have not been able to recognize your IP address 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
or by using our contact form.

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

exceptional Lie algebras, Freudenthal–Tits magic square, octonions
Mathematical Subject Classification
Primary: 20G41
Received: 11 April 2022
Revised: 26 September 2022
Accepted: 26 October 2022
Published: 13 September 2023
Robert A. Wilson
School of Mathematical Sciences
Queen Mary University of London
United Kingdom
Tevian Dray
Department of Mathematics
Oregon State University
Corvallis, OR
United States
Corinne A. Manogue
Department of Physics
Oregon State University
Corvallis, OR
United States