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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A quaternionic construction of $E_7$
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by Robert A. Wilson PDF
Proc. Amer. Math. Soc. 142 (2014), 867-880 Request permission

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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Additional Information
  • Robert A. Wilson
  • Affiliation: School of Mathematical Sciences, Queen Mary University of London, Mile End Road, London E1 4NS, United Kingdom
  • MR Author ID: 209865
  • Email: R.A.Wilson@qmul.ac.uk
  • 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
  • © Copyright 2013 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 142 (2014), 867-880
  • MSC (2010): Primary 20G20, 20D06
  • DOI: https://doi.org/10.1090/S0002-9939-2013-11838-1
  • MathSciNet review: 3148521