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The algebraic classification of $7$-dimensional nilpotent $3$-Lie algebras | ||
| Journal of Algebra and Related Topics | ||
| دوره 14، Special Issue- Dedicated to the memory of Jürgen Herzog (1941-2024).، تیر 2026، صفحه 59-80 اصل مقاله (195.28 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22124/jart.2025.28277.1703 | ||
| نویسنده | ||
| H. Darabi* | ||
| Department of Mathematics, Esfarayen University of Technology, Esfarayen, Iran | ||
| چکیده | ||
| This paper focuses on the classification of $7$-dimensional nilpotent $3$-Lie algebras. We employ a systematic approach by considering the structure of these algebras through the central ideals. Specifically, we divide the $7$-dimensional nilpotent $3$-Lie algebra by a $1$-dimensional central ideal, resulting in a $6$- dimensional nilpotent $3$-Lie algebra. Our findings reveal the relationships between $7$-dimensional structures and their $6$-dimensional counterparts, contributing to a deeper understanding of the properties and classifications of nilpotent $3$-Lie algebras. | ||
| کلیدواژهها | ||
| Nilpotent $n$-Lie algebra؛ Algebraic classification؛ Low dimensions | ||
| مراجع | ||
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