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Journals / Celal Bayar Üniversitesi Fen Bilimleri Dergisi / 2023 / Cilt: 19 Sayı: 4

On 7-Dimensional Nilpotent Leibniz Algebras With 1-Dimensional Leib Ideal

İsmail Demir(UŞAK ÜNİVERSİTESİ)0000-0002-8070-6489
Pages
343–349
Publication Date
2023-12-29
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AI Summary & Key Takeaways

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

Certain cases of seven-dimensional complex nilpotent Leibniz algebras of those with one-dimensional Leib ideal and derived algebra of codimension two are classified.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Leibniz algebras are nonanticommutative versions of Lie algebras.
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Key Findings & Data:Lie algebras have many applications in many scientific areas as well as mathematical areas.
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Conclusion & Impact:Certain cases of seven-dimensional complex nilpotent Leibniz algebras of those with one-dimensional Leib ideal and derived algebra of codimension two are classified.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:Bilinear forms · Classification · Leibniz algebra

Abstract

Leibniz algebras are nonanticommutative versions of Lie algebras. Lie algebras have many applications in many scientific areas as well as mathematical areas. Scientists from different disciplines have used specific examples of Lie algebras according to their needs. However, we mathematicians are more interested in generality than in obtaining a few examples. The classification problem for Leibniz algebras has an intrinsically wild nature as in Lie algebras. In this article, the approach of congruence classes of bilinear forms is extended to classify certain subclasses of seven-dimensional nilpotent Leibniz algebras over complex numbers. Certain cases of seven-dimensional complex nilpotent Leibniz algebras of those with one-dimensional Leib ideal and derived algebra of codimension two are classified.

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Cite This Article

Demir, İ. (2023). On 7-Dimensional Nilpotent Leibniz Algebras With 1-Dimensional Leib Ideal. Celal Bayar Üniversitesi Fen Bilimleri Dergisi, Cilt: 19 Sayı: 4, 343–349. https://doi.org/10.18466/cbayarfbe.1339702

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