CIdeals of Lie Algebras
Abstract
A subalgebra B of a Lie algebra L is called a cideal of L if there is an ideal C of L such that L = B + C and B \cap C \leq B_L, where B_L is the largest ideal of $L$ contained in B. This is analogous to the concept of cnormal subgroup, which has been studied by a number of authors. We obtain some properties of cideals and use them to give some characterisations of solvable and supersolvable Lie algebras. We also classify those Lie algebras in which every onedimensional subalgebra is a cideal.
 Publication:

arXiv eprints
 Pub Date:
 November 2008
 arXiv:
 arXiv:0811.2689
 Bibcode:
 2008arXiv0811.2689T
 Keywords:

 Mathematics  Rings and Algebras;
 17B05;
 17B20;
 17B30;
 17B50.
 EPrint:
 12 pages