On the structure of split involutive regular Hom-Lie algebras

We study the strucure of arbitrary split involutive regular Hom-Lie algebras. By developing techniques of connections of roots for this kind of algebras, we show that such an algebra L is of the form (Formula presented) with U a subspace of the involutive abelian subalgebra H and any I_[j], a well described involutive ideal of L, satisfying [I_[j], I_[k]] =0 if [ j] ≠[k]. Under certain conditions, in the case of L being of maximal length, the simplicity of the algebra is characterized and it is shown that L is the direct sum of the family of its minimal involutive ideals, each one being a simple split involutive regular Hom-Lie algebra.