A note on the Schur multiplier of a nilpotent Lie algebra

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

2010-01-04

arxiv.org/abs/1001.0176v3

Comm. Algebra 39 (2011), 1293--1297

Mathematics

Rings and Algebras

Paper in press in Comm. Algebra with small revisions

Scientific paper

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.

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