# A note on the Schur multiplier of a nilpotent Lie algebra

Francesco Russo, Peyman Niroomand

Risultato della ricerca: Article

31 Citazioni (Scopus)

### Abstract

For a nilpotent Lie algebra $L$ of dimension $n$ and dim$(L^2)=m$, we find the upper bound dim$(M(L))\leq {1/2}(n+m-2)(n-m-1)+1$, where $M(L)$ denotes the Schur multiplier of $L$. In case $m=1$ the equality holds if and only if $L\cong H(1)\oplus A$, where $A$ is an abelian Lie algebra of dimension $n-3$ and H(1) is the Heisenberg algebra of dimension 3.
Lingua originale English 1293-1297 5 Communications in Algebra 39 Published - 2011

### All Science Journal Classification (ASJC) codes

• Algebra and Number Theory