Lie algebras whose lattice of ideals is closely related with a subspace lattice |
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Authors: | M.P. Benito |
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Affiliation: | Departamento de Matemáticas, Estadística y Computatión , Untversidad de la rioja , Edihcio de magisterio. Luis de Ulloa s/n, LOGRO?O (LA RIOJA), 26004, Spain |
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Abstract: | Relationships between the structure of a Lie algebra and that of its lattice of ideals is studied for those Lie algebras whose ideal lattice is very close to that of an almost-abelian Lie algebra. It is shown here that if the base field is algebraically closed, finite or the real one, for any n ≥3 the only solvable Lie algebra whose lattice of ideals is isomorphic to that of the (n+l)-dimensional almost-abelian Lie algebra is itself. |
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