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Lattice isomorphic solvable Lie algebras

Published online by Cambridge University Press:  09 April 2009

R. C. Glaeser  and
B. Kolman
R. C. Glaeser
Affiliation:
Temple University, Philadelphia, Pa.
B. Kolman
Affiliation:
Drexel Institute of Technology, Philadelphia, Pa.
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Let L be a Lie algebra over a field κ of any characteristic, and consider the lattice ℒ(L) of all subalgebras of L. In this paper we prove that if L and M are lattice isomorphic Lie algebras, over a field of any characteristic, and L′ and M′ are nilpotent, then the difference between the orders of solvability of L and M differs by at most one.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 10 , Issue 3-4 , November 1969 , pp. 266 - 268
Copyright
Copyright © Australian Mathematical Society 1969

References

[1]Barnes, D. W., ‘Lattice Isomorphisms of Lie Algebras’, J. Austral. Math. Soc. 4 (1964), 470–475.Google Scholar
[2]Barnes, D. W., and Wall, G. E., ‘On Normalizer Preserving Lattice Isomorphisms Between Nilpotent Groups’, J. Austral. Math. Soc. 4 (1964), 454–69.Google Scholar
[3]Kolman, B., ‘Semi-modular Lie Algebras’, J. Sci. Hiroshima Univ. Ser. A-I 29 (1965), 149–63.Google Scholar