Biderivations serve as bilinear mappings that satisfy derivation conditions in each argument of a Lie algebra. They offer a refined tool to probe the structure of Lie algebras, delineating both inner ...

The purpose of this paper is to give a classification of the orbits in a real reductive Lie algebra under the adjoint action of a corresponding connected Lie group. The classification is obtained by ...

It is proved that in a free nilpotent Lie algebra there are no nonabelian ideals which are free nilpotent as subalgebras. It is also shown that, for any proper ideal S of a free Lie algebra F, the ...