A δ-first Whitehead Lemma

The Whitehead First Lemma for Alternative

Converse Second Whitehead Lemma

We show that finite-dimensional Lie algebras over a field of characteristic zero such that the second cohomology group in every finite-dimensional module vanishes, are, essentially, semisimple.

A Converse to the Third Whitehead Lemma

We show that finite-dimensional Lie algebras over a field of characteristic zero such that their high-degree cohomology in any finite-dimensional non-trivial irreducible module vanishes, are, essentially, direct sums of semisimple and nilpotent algebras. The classical First and Second Whitehead Lemmata state that the first, respectively second, cohomology group of a finite-dimensional semisimpl...

A Converse to the Second Whitehead Lemma

We show that finite-dimensional Lie algebras over a field of characteristic zero such that the second cohomology group in every finite-dimensional module vanishes, are, essentially, semisimple.

The First Almost Free Whitehead Group Sh914

Assume G.C.H. and κ is the first uncountable cardinal such that there is a non-free κ-free abelian Whitehead group of cardinality κ. We prove that if all κ-free Abelian group of cardinality κ are Whitehead then κ is necessarily an inaccessible cardinal.