C-Ideals of Lie Algebras |
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Authors: | David A. Towers |
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Affiliation: | 1. Department of Mathematics , Lancaster University , Lancaster, England, UK d.towers@lancaster.ac.uk |
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Abstract: | 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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Keywords: | C-Ideal Frattini ideal Lie algebras Nilpotent Solvable Supersolvable |
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