A radical for graded Lie algebras

Abstract

For an arbitrary group G and a G-graded Lie algebra L over a field of characteristic zero we show that the Kostrikin radical of L is graded and coincides with the graded Kostrikin radical of L. As an important tool for our proof we show that the graded Kostrikin radical is the intersection of all gradedstrongly prime ideals of L. In particular, graded-nondegenerate Lie algebras are subdirect products of graded-strongly prime Lie algebras.