Automorphisms and derivations of abelian extensions of some Lie algebras
Let \(L\) be a free Lie algebra, \(R\) an ideal of \(L\). An automorphism \(L/R\) is called tame if it is induced by an automorphism of \(L\) leaving \(R\) invariant. The authors prove that if \(K\) is an integral domain and \(M_ n= L/(L^ 2)^ 2\) a free metabelian algebra over \(K\) of rank \(n\), then any inner automorphism \(e^{\text{ad z}}\), \(z\in M^ 2\), is not tame. They consider similar problems for abelian extensions and derivation algebras and in particular, they prove that the derivation algebra \(\text{Der} M_ n\) of the free metabelian algebra of rank \(n>1\) is not finitely generated.
scientific article; zbMATH DE number 404307