C-Ideals of Lie Algebras

@article{Towers2008CIdealsOL,
title={C-Ideals of Lie Algebras},
author={David A. Towers},
journal={Communications in Algebra},
year={2008},
volume={37},
pages={4366 - 4373}
}
• D. Towers
• Published 17 November 2008
• Mathematics
• Communications in Algebra
A subalgebra B of a Lie algebra L is called a c-ideal of L if there is an ideal C of L such that L = B + C and B ∩ C ≤ B L , where B L is the largest ideal of L contained in B. This is analogous to the concept of c-normal subgroup, which has been studied by a number of authors. We obtain some properties of c-ideals and use them to give some characterisations of solvable and supersolvable Lie algebras. We also classify those Lie algebras in which every one-dimensional subalgebra is a c-ideal.
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