A note on strongly split Lie algebras

Abstract

Split Lie algebras are maybe the most known examples of graded Lie algebras. Since an important category in the class of graded algebras is the category of strongly graded algebras, we introduce, in a natural way, the category of strongly split Lie algebras $L$ and show that if $L$ is centerless, then $L$ is the direct sum of split ideals each of which is a split-simple strongly split Lie algebra.