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C-Ideals of Lie Algebras.

By David A. Towers

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 \cap C \leq 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

Year: 2009
OAI identifier: oai:eprints.lancs.ac.uk:19877
Provided by: Lancaster E-Prints

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