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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 53 Issue: 1

On classification of $7$-dimensional odd-nilpotent Leibniz algebras

İsmail Demir(USAK UNIVERSITY)0000-0002-8070-6489
Pages
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Publication Date
2024-02-29
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Odd-nilpotent Leibniz algebras are defined as that its even dimensional ideals in lower central series are all zero and the classification of $7-$dimensional complex odd-nilpotent Leibniz algebras with one dimensional Leib ideal is obtained by applying the aforementioned method.

📌 3 Key Takeaways

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Objective & Hypothesis:In this paper we extend the method of canonical form for congruence of bilinear forms to give the classification of some subclasses of $7-$dimensional nilpotent Leibniz algebras.
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Key Findings & Data:In this paper we extend the method of canonical form for congruence of bilinear forms to give the classification of some subclasses of $7-$dimensional nilpotent Leibniz algebras.
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Conclusion & Impact:Odd-nilpotent Leibniz algebras are defined as that its even dimensional ideals in lower central series are all zero and the classification of $7-$dimensional complex odd-nilpotent Leibniz algebras with one dimensional Leib ideal is obtained by applying the aforementioned method.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Leibniz algebra · nilpotency · classification

Abstract

In this paper we extend the method of canonical form for congruence of bilinear forms to give the classification of some subclasses of $7-$dimensional nilpotent Leibniz algebras. Odd-nilpotent Leibniz algebras are defined as that its even dimensional ideals in lower central series are all zero and the classification of $7-$dimensional complex odd-nilpotent Leibniz algebras with one dimensional Leib ideal is obtained by applying the aforementioned method.

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Cite This Article

Demir, İ. (2024). On classification of $7$-dimensional odd-nilpotent Leibniz algebras. Hacettepe Journal of Mathematics and Statistics, Volume: 53 Issue: 1. https://doi.org/10.15672/hujms.1185538

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References (10)

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