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 ...

We establish an irreducibility property for the characters of finite dimensional, irreducible representations of simple Lie algebras (or simple algebraic groups) over the complex numbers, i.e., that ...

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 ...