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Lie algebras all of whose maximal subalgebras have codimension one

Published online by Cambridge University Press:  20 January 2009

David Towers
David Towers
Affiliation:
Department of Mathematics, University of Lancaster, Lancaster LA1 4YL, England Department of Mathematics, University of California, Berkeley, CA 94720, USA
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Let denote the class of finite-dimensional Lie algebras L (over a fixed, but arbitrary, field F) all of whose maximal subalgebras have codimension 1 in L. In (2) Barnes proved that the solvable algebras in are precisely the supersolvable ones. The purpose of this paper is to extend this result and to give a characterisation of all of the algebras in . Throughout we shall place no restrictions on the underlying field of the Lie algebra.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 24 , Issue 3 , October 1981 , pp. 217 - 219
Copyright
Copyright © Edinburgh Mathematical Society 1981

References

REFERENCES

(1)Amayo, R. K., Quasi-ideals of Lie algebras II, Proc. London Math. Soc. (3) 33 (1976), 37–64.Google Scholar
(2)Barnes, D. W., On the cohomology of soluble Lie algebras, Math. Z. 101 (1967), 343–349.Google Scholar
(3)Towers, D. A., A Frattini theory for algebras, Proc. London Math. Soc. (3) 27 (1973), 440–462.CrossRefGoogle Scholar