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On ideally finite Lie algebras which are lower semi-modular

Published online by Cambridge University Press:  20 January 2009

David Towers
David Towers
Affiliation:
Department of MathematicsUniversity of LancasterLancasterLA1 4YL
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The purpose of this paper is twofold: first to correct the statement of Theorem 1 in [4], and secondly to consider related problems in the class of ideally finite Lie algebras.

Throughout, L will denote a Lie algebra over a field K, F(L) will be its Frattini subalgebra and φ(L) its Frattini ideal. We will denote by the class of Lie algebras all of whose maximal subalgebras have codimension 1 in L. The Lie algebra with basis {u–1, u0, u1} and multiplication u–1u0 = u–1, u–1u1 = u0, u0u1 = u1 will be labelled L1(0).

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 28 , Issue 1 , February 1985 , pp. 9 - 11
Copyright
Copyright © Edinburgh Mathematical Society 1985

References

REFERENCES

1.Barnes, D. W., On the cohomology of soluble Lie algebras, Math. Z. 101 (1967) 343–349.Google Scholar
2.Gein, A. G., Semimodular Lie algebras, Siberian Math. J. 17 (1976), 189–193.CrossRefGoogle Scholar
3.Stewart, I. N., Lie algebras generated by finite-dimensional ideals (Pitman 1975).Google Scholar
4.Towers, D. A., Lie algebras, all of whose maximal subalgebras have codimension 1, Proc. Edinburgh Math. Soc. 24 (1981), 217–219.CrossRefGoogle Scholar