On split Lie superalgebras

We study the structure of arbitrary split Lie superalgebras. We show that any of such superalgebras L is of the form L=U+Sigma(j)I(j) with U a subspace of the Abelian (graded) subalgebra H and any I(j), a well described (graded) ideal of L satisfying [I(j),I(k)]=0 if j not equal k. Under certain conditions, the simplicity of L is characterized and it is shown that L is the direct sum of the family of its minimal (graded) ideals, each one being a simple split Lie superalgebra. (C) 2010 American Institute of Physics. [doi:10.1063/1.3464265]