Nilpotent-by-abelian Lie algebras of type FPm

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Let L be a finitely generated Lie algebra which is a split extension of a free nilpotent Lie algebra N by a finite dimensional abelian Lie algebra. Let V denote the quotient of N by its commutator subalgebra; we can regard V as a module for L/N. We discuss the relationship between the homological finiteness properties of V and those of L. In particular, we show that if L has type F P, and N has class c then V is 1 + c(m - 1)-tame (equivalently, the (1 + c(m - 1))th tensor power of V is finitely generated under the diagonal action of L/N).o TEXTO COMPLETO DESTE ARTIGO, ESTARÁ DISPONÍVEL À PARTIR DE AGOSTO DE 2015.1483429437Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq