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On normed Lie algebras with sufficiently many subalgebras of codimension I

Published online by Cambridge University Press:  20 January 2009

E. V. Kissin
E. V. Kissin
Affiliation:
Department of Mathematics Statistics and Computing, The Polytechnic of North London, Holloway, London N7 8DB
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Let H be a finite or infinite dimensional Lie algebra. Barnes [2] and Towers [5] considered the case when H is a finite-dimensional Lie algebra over an arbitrary field, and all maximal subalgebras of H have codimension 1. Barnes, using the cohomology theory of Lie algebras, investigated solvable algebras, and Towers extended Barnes's results to include all Lie algebras. In [4] complex finite-dimensional Lie algebras were considered for the case when all the maximal subalgebras of H are not necessarily of codimension 1 but when

where S(H) is the set of all Lie subalgebras in H of codimension 1. Amayo [1]investigated the finite-dimensional Lie algebras with core-free subalgebras of codimension 1 and also obtained some interesting results about the structure of infinite dimensional Lie algebras with subalgebras of codimension 1.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 29 , Issue 2 , June 1986 , pp. 199 - 220
Copyright
Copyright © Edinburgh Mathematical Society 1986

References

REFERENCES

1Amayo, R. K., Quasi-ideals of Lie algebras II, Proc. London Math. Soc. (3) 33 (1976), 37–64.CrossRefGoogle Scholar
2Barnes, D. W., On the cohomology of soluble algebras, Math. Z. 101 (1967), 343–349.CrossRefGoogle Scholar
3Dixmier, J., Les C*-algebras et leurs representations (Gauthier-Villars Editeur, Paris, 1969).Google Scholar
4Kissin, E. V., On some reflexive algebras of operators and the operator Lie algebras of their derivations, Proc. London Math. Soc. (3) 49 (1984), 1–35.CrossRefGoogle Scholar
5Towers, D., Lie algebras all of whose maximal subalgebras have codimension one, Proc. Edinburgh Math. Soc. 24 (1981), 217–219.CrossRefGoogle Scholar