Some results on the Schur multiplier of nilpotent Lie algebras

For a non-abelian Lie algebra \(L\) of dimension \(n\) with the derived subalgebra of dimension \(m\) , the first author earlier proved that the dimension of its Schur multiplier is bounded by \(\frac{1}{2}(n+m-2)(n-m-1)+1\). In the current work, we give some new inequalities on the exterior square...

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Veröffentlicht in:arXiv.org 2017-01
Hauptverfasser: Niroomand, Peyman, Johari, Farangis
Format: Artikel
Sprache:eng
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Zusammenfassung:For a non-abelian Lie algebra \(L\) of dimension \(n\) with the derived subalgebra of dimension \(m\) , the first author earlier proved that the dimension of its Schur multiplier is bounded by \(\frac{1}{2}(n+m-2)(n-m-1)+1\). In the current work, we give some new inequalities on the exterior square and the Schur multiplier of Lie algebras and then we obtain the class of all nilpotent Lie algebras which attains the above bound. Moreover, we also improve this bound as much as possible.
ISSN:2331-8422
DOI:10.48550/arxiv.1701.03956