University of Guilan Journal of Algebra and Related Topics 2345-3931 14 Special Issue- Dedicated to the memory of Jürgen Herzog (1941-2024). 2026 04 01 The algebraic classification of $7$-dimensional nilpotent $3$-Lie algebras 59 80 8848 10.22124/jart.2025.28277.1703 EN H. Darabi Department of Mathematics, Esfarayen University of Technology, Esfarayen, Iran Journal Article 2024 08 25 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. https://jart.guilan.ac.ir/article_8848_f7ce8eeaf3ed912543ffa45fc2ccb137.pdf