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RESEARCH PRODUCT

A note on the Schur multiplier of a nilpotent Lie algebra

Peyman NiroomandFrancesco G. Russo

subject

Pure mathematicsAlgebra and Number TheoryDimension (graph theory)Schur multiplier nilpotent Lie algebrasMathematics - Rings and AlgebrasUpper and lower boundsNilpotent Lie algebraSettore MAT/02 - Algebra17B30 17B60 17B99Rings and Algebras (math.RA)Lie algebraFOS: MathematicsSettore MAT/03 - GeometriaAlgebra over a fieldAbelian groupMathematicsSchur multiplier

description

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.

yearjournalcountryeditionlanguage
2011-03-21
https://dx.doi.org/10.48550/arxiv.1001.0176