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

Francesco Russo, Peyman Niroomand

Research output: Contribution to journalArticlepeer-review

42 Citations (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.
Original language English 1293-1297 5 Communications in Algebra 39 Published - 2011

## All Science Journal Classification (ASJC) codes

• Algebra and Number Theory

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