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Mathematical Proceedings of the Cambridge Philosophical Society Mathematical Proceedings of the Cambridge Philosophical Society

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On the compact real form of the Lie algebra 2

Published online by Cambridge University Press:  29 October 2009

ROBERT A. WILSON
ROBERT A. WILSON
Affiliation:
School of Mathematical Sciences, Queen Mary University of London, Mile End Road, London E 1 4 NS. e-mail: r.a.wilson@qmul.ac.uk
Corresponding
E-mail address:
r.a.wilson@qmul.ac.uk
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Abstract

We give an elementary construction of the compact real form of the Lie algebra 2. This construction exhibits the group 23·L3(2) as a group of automorphisms. We also show that there is a unique 14-dimensional real Lie algebra invariant under the action of this group.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 148 , Issue 1 , January 2010 , pp. 87 - 91
Copyright
Copyright © Cambridge Philosophical Society 2009

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References

[1]Borovik, A. V.Jordan subgroups of simple algebraic groups (Russian). Algebra i Logika 28 (1989), 144–159, 244.Google Scholar
[2]Borovik, A. V.Jordan subgroups and orthogonal decompositions (Russian). Algebra i Logika 28 (1989), 382–392, 486.CrossRefGoogle Scholar
[3]Jacobson, N.Lie Algebras (Wiley, 1962; Dover reprint, 1979).Google Scholar
[4]Kostrikin, A. I. and Tiep, P. H.Orthogonal decompositions and integral lattices. de Gruyter Expositions in Mathematics, 15 (Walter de Gruyter & Co., 1994).CrossRefGoogle Scholar
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[6]Wilson, R. A. An elementary construction of the Ree groups of type 2G 2. Proc. Edinburgh Math. Soc., to appear.Google Scholar
[7]Wilson, R. A. On the compact real form of the Lie algebra 4. In preparation.Google Scholar

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