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.References
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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