Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-29T18:58:00.716Z Has data issue: false hasContentIssue false

On the compact real form of the Lie algebra 2

Published online by Cambridge University Press:  29 October 2009

ROBERT A. WILSON*
Affiliation:
School of Mathematical Sciences, Queen Mary University of London, Mile End Road, London E 1 4 NS. e-mail: [email protected]

Abstract

We give an elementary construction of the compact real form of the Lie algebra 2. This construction exhibits the group 2L3(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
Copyright
Copyright © Cambridge Philosophical Society 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Borovik, A. V.Jordan subgroups of simple algebraic groups (Russian). Algebra i Logika 28 (1989), 144159, 244.Google Scholar
[2]Borovik, A. V.Jordan subgroups and orthogonal decompositions (Russian). Algebra i Logika 28 (1989), 382392, 486.Google 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
[5]Thompson, J. G.A conjugacy theorem for E 8. J. Algebra 38 (1976), 525530.CrossRefGoogle Scholar
[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