Weak c-ideals of Lie algebras

2020/06/09 by Towers, David A., Ciloglu, Zekiye
#FOS: Mathematics #Group Theory (math.GR) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2006.05234

Abstract

A subalgebra B of a Lie algebra L is called a weak c-ideal of L if there is a subideal 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 weakly c- normal subgroups, which has been studied by a number of authors. We obtain some properties of weak c-ideals and use them to give some characterisations of solvable and supersolvable Lie algebras. We also note that one-dimensional weak c-ideals are c-ideals.

Related

• C-Ideals of Lie Algebras
• Weak c-ideals of Leibniz algebras
• C-sections of Lie algebras
• Three Minimax Ideal Relations of Lie Algebras
• On the Lie ideals of C*-algebras