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Almost nilpotent Lie algebras

Published online by Cambridge University Press:  18 May 2009

David A. Towers
David A. Towers
Affiliation:
Department of Mathematics, University of Lancaster, Bailrigg Lancaster, LA1 4YL
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Throughout we shall consider only finite-dimensional Lie algebras over a field of characteristic zero. In [3] it was shown that the classes of solvable and of supersolvable Lie algebras of dimension greater than two are characterised by the structure of their subalgebra lattices. The same is true of the classes of simple and of semisimple Lie algebras of dimension greater than three. However, it is not true of the class of nilpotent Lie algebras. We seek here the smallest class containing all nilpotent Lie algebras which is so characterised.

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 29 , Issue 1 , January 1987 , pp. 7 - 11
Copyright
Copyright © Glasgow Mathematical Journal Trust 1987

References

REFERENCES

1.Kolman, B., Semi-modular Lie algebras, J. Sci. Hiroshima Univ. Ser. A-I Math. 29 (1965), 149–163.Google Scholar
2.Towers, D. A., A Frattini theory for algebras, Proc. London Math. Soc. (3) 27 (1973), 440–462.CrossRefGoogle Scholar
3.Towers, D. A., Lattice isomorphisms of Lie algebras, Math. Proc. Cambridge Philos. Soc. 89 (1981), 285–292; and, corrigenda, 95 (1984), 511–512.CrossRefGoogle Scholar