Algebras de Lie finitamente apresentaveis

by da Silva, Viviane Moretto

In this work we study the classification of finitely presented abelian-by-finite dimensional Lie algebras given in [4]. If L is a Lie algebra, an extension of an abelian ideal A by a finite dimensional Lie algebra L/A then L is finitely presented if and only if A X A is finitely generated as U(L/A)-module via the diagonal action, where U(L/A) is the universal enveloping algebra of L/A. We study in detail the result that finite generation of A X A over U(L/A) implies finite presentability of L