A restriction on the Schur multiplier of nilpotent Lie algebras

An improvement of a bound of Yankosky (2003) is presented in this paper, thanks to a restriction which has been recently obtained by the authors on the Schur multiplier $M (L)$ of a finite dimensional nilpotent Lie algebra $L$. It is also described the structure of all nilpotent Lie algebras such that the bound is attained. An important role is played by the presence of a derived subalgebra of maximal dimension. This allows precision on the size of $M (L)$. Among other results, applications to the non-abelian tensor square $L \otimes L$ are illustrated.