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A quaternionic construction of $ E_7$

Author: Robert A. Wilson
Journal: Proc. Amer. Math. Soc. 142 (2014), 867-880
MSC (2010): Primary 20G20, 20D06
Published electronically: December 26, 2013
MathSciNet review: 3148521
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Abstract: We give an explicit construction of the simply-connected compact real form of the Lie group of type $ E_7$, as a group of $ 28\times 28$ matrices over quaternions, acting on a $ 28$-dimensional left quaternion vector space. This leads to a description of the simply-connected split real form, acting on a $ 56$-dimensional real vector space, and thence to the finite quasi-simple groups of type $ E_7$. The sign problems usually associated with constructing exceptional Lie groups are almost entirely absent from this approach.

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Robert A. Wilson
Affiliation: School of Mathematical Sciences, Queen Mary University of London, Mile End Road, London E1 4NS, United Kingdom

Received by editor(s): February 9, 2012
Received by editor(s) in revised form: April 21, 2012, and April 25, 2012
Published electronically: December 26, 2013
Communicated by: Pham Huu Tiep
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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