Journal of Lie Theory

no. 3
Abelian Ideals of Maximal Dimension for Solvable Lie Algebras
Dietrich Burde1; Manuel Ceballos2
1Fakultät für Mathematik, Universität Wien, Nordbergstr. 15, 1090 Wien, Austria
2Dep. Geometria y Topologia, Universidad de Sevilla, Sevilla, Spain
Journal of Lie Theory, Volume 22 (2012) no. 3, pp. 741-756
We compare the maximal dimension of abelian subalgebras and the maximal dimension of abelian ideals for finite-dimensional Lie algebras. We show that these dimensions coincide for solvable Lie algebras over an algebraically closed field of characteristic zero. We compute this invariant for all complex nilpotent Lie algebras of dimension n ≤ 7. Furthermore we study the case where there exists an abelian subalgebra of codimension 2. Here we explicitly construct an abelian ideal of codimension 2 in case of nilpotent Lie algebras.
DOI: 10.5802/jolt.689
Classification: 17B30, 17D25
Keywords: Abelian ideals, abelian subalgebras, degenerations

Dietrich Burde  1 ; Manuel Ceballos  2

1 Fakultät für Mathematik, Universität Wien, Nordbergstr. 15, 1090 Wien, Austria
2 Dep. Geometria y Topologia, Universidad de Sevilla, Sevilla, Spain 
Dietrich Burde; Manuel Ceballos. Abelian Ideals of Maximal Dimension for Solvable Lie Algebras. Journal of Lie Theory, Volume 22 (2012) no. 3, pp. 741-756. doi: 10.5802/jolt.689
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     title = {Abelian {Ideals} of {Maximal} {Dimension} for {Solvable} {Lie} {Algebras}},
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     pages = {741--756},
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