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Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

 

 

$ E_8$, the most exceptional group


Author: Skip Garibaldi
Journal: Bull. Amer. Math. Soc. 53 (2016), 643-671
MSC (2010): Primary 20G41; Secondary 17B25, 20G15
DOI: https://doi.org/10.1090/bull/1540
Published electronically: June 29, 2016
MathSciNet review: 3544263
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Abstract: The five exceptional simple Lie algebras over the complex number are included one within the other as $ \mathfrak{g}_2 \subset \mathfrak{f}_4 \subset \mathfrak{e}_6 \subset \mathfrak{e}_7 \subset \mathfrak{e}_8$. The biggest one, $ \mathfrak{e}_8$, is in many ways the most mysterious. This article surveys what is known about it, including many recent results, and it focuses on the point of view of Lie algebras and algebraic groups over fields.


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Additional Information

Skip Garibaldi
Affiliation: Center for Communications Research, San Diego, California 92121
Email: skip@member.ams.org

DOI: https://doi.org/10.1090/bull/1540
Received by editor(s): December 28, 2015
Published electronically: June 29, 2016
Article copyright: © Copyright 2016 American Mathematical Society