2008/11/17 by David A. Towers, Towers, David A.
Mathematics · #17B05 #17B20 #17B30 #17B50. #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA #msc:17B05 #msc:17B20 #msc:17B30 #msc:17B50.
paper · pdf · doi:10.48550/arxiv.0811.2689
12 pages
arxiv created 2008/11/17 · arxiv updated 2009/12/01
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 ≤ BL, where BL 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.