Bulletin of the Australian Mathematical Society

Research Article

ON LEVI’S THEOREM FOR LEIBNIZ ALGEBRAS

DONALD W. BARNESa1

a1 1 Little Wonga Rd, Cremorne, NSW 2090, Australia (email: donwb@iprimus.com.au)

Abstract

A Lie algebra over a field of characteristic 0 splits over its soluble radical and all complements are conjugate. I show that the splitting theorem extends to Leibniz algebras but that the conjugacy theorem does not.

(Received September 22 2011)

2010 Mathematics subject classification

  • primary 17A32

Keywords and phrases

  • Leibniz algebras;
  • Levi’s theorem