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The algebraic classification of $7$-dimensional nilpotent $3$-Lie algebras | ||
| Journal of Algebra and Related Topics | ||
| دوره 14، S1، 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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[1] M. A. Alvarez, Degenerations of 8-dimensional 2-step nilpotent Lie algebras, Algebr. Represent. Theory, (5) 24 (2021), 1231–1243. [2] R. Bai, G. Song and Y. Zhang, On classification of n-Lie algebras, Front. Math. China, (4) 6 (2011), 581–606. [3] N. Cantarini and V. G. Kac, Classification of simple linearly compact n-Lie superalgebras, Comm. Math. Phys., (3) 298 (2010), 833–853. [4] R. Carles and Y. Diakit´e, Sur les vari´et´es d’alg`ebres de Lie de dimension 7. (French) [Varieties of Lie algebras of dimension 7], J. Algebra, (1) 91 (1984), 53–63. [5] S. Cicalo, W. A. de Graaf and C. Schneider, Six-dimensional nilpotent Lie algebras, Linear Algebra Appl., (1) 436 (2012), 163–189. [6] H. Darabi, M. Eshrati and F. Saeedi, The algebraic classification of low-dimensional nilpotent n-Lie algebras, Asian-Eur. J. Math., (3) 18 (2025), 2450110. [7] H. Darabi and M. Imanparast, On classification of 9-dimensional nilpotent 3-ary algebras of class two, Bull. Iranian Math. Soc., 47 (2021), 929–937. [8] H. Darabi, F. Saeedi and M. Eshrati, A characterization of finite dimensional nilpotent Filippov algebras, J. Geom. Phys., 101 (2016), 100–107. [9] M. Eshrati, F. Saeedi and H. Darabi, On the multiplier of nilpotent n-Lie algebras, J. Algebra, 450 (2016), 162–172. [10] V. T. Filippov, n-Lie algebras, Sib. Math. J, (6) 26 (1985), 879–891. [11] M. P. Gong, Classification of Nilpotent Lie Algebras of Dimension 7 (Over Algebraically Closed Fields and R), Ph.D. Thesis, University of Waterloo, Waterloo, (1998). [12] W. A. de Graaf, Classification of 6-dimensional nilpotent Lie algebras over fields of characteristic not 2, J. Algebra (2) 309 (2007), 640–653. [13] F. Grunewald and J. O’Halloran, Varieties of nilpotent Lie algebras of dimension less than six, J. Algebra, (2) 112 (1988), 315–325. [14] A. S. Hegazi and H. Abdelwahab, Classification of five-dimensional nilpotent Jordan algebras, Linear Algebra Appl., 494 (2016), 165–218. [15] Z. Hoseini, F. Saeedi and H. Darabi, On Classification of (n+5)-dimensional nilpotent n-Lie algebras of class two, Bull. Iranian Math. Soc., (4) 45 (2019), 939–949. [16] N. Ismailov, I. Kaygorodov and Y. Volkov, The geometric classification of Leibniz algebras, Internat. J. Math., (5) 29 (2018), 1850035. [17] M. Jamshidi, F. Saeedi and H. Darabi, On classification of (n+6)-dimensional nilpotent n-Lie algebras of class two with n ≥ 4, Arab J. Math. Sci., (2) 27 (2021), 139–150. [18] S. M. Kasymov, Theory of n-Lie algebras, Algebra Logic, (3) 26 (1987), 155–166. [19] I. Kaygorodov, M. Khrypchenko and S. A. Lopes, The algebraic and geometric classification of nilpotent anticommutative algebras, J. Pure Appl. Algebra, (8) 224 (2020), 106337. [20] I. Kaygorodov, M. Khrypchenko and Y. Popov, The algebraic and geometric classification of nilpotent terminal algebras, J. Pure Appl. Algebra, (6) 225 (2021), 106625. [21] I. Kaygorodov and Y. Volkov, Degenerations of Filippov algebras, J. Math. Phys., (2) 61 (2020), 021701. [22] I. Kaygorodov and Y. Volkov, Degenerations of noncommutative Heisenberg algebras, Comm. Algebra, (10) 51 (2023), 4204–4213. [23] W. Ling, On Structure of n-Lie Algebras, Ph.D. thesis, University-GHS-Siegen, (1993). [24] G. Mazzola, The algebraic and geometric classification of associative algebras of dimension five, Manuscripta Math., (1) 27 (1979), 81–101. [25] V. V. Morozov, Classification of nilpotent Lie algebras of sixth order, Izv. Vyssh. Uchebn. Zaved. Mat., 4 (1958), 161–171. [26] A. P. Pozhidaev, On simple n-Lie algebras, Algebra Logic, (3) 38 (1999), 181–192. [27] B. Ren and D. J. Meng, Some 2-step nilpotent Lie algebras I, Linear Algebra Appl., 338 (2001), 77–98. [28] B. Ren and L. S. Zhu, Classification of 2-step nilpotent Lie algebras of dimension 8 with 2-dimensional center, Comm. Algebra, (6) 39 (2011), 2068–2081. [29] B. Ren and L. S. Zhu, Classification of 2-step nilpotent Lie algebras of dimension 9 with 2-dimensional center, Czechoslovak Math. J., (3) 67 (2017), 953–965. [30] C. Seeley, 7-dimensional nilpotent Lie algebras, Trans. Amer. Math. Soc., (2) 335 (1993), 479–496. [31] K. A. Umlauf, Ueber den Zusammenhang der endlichen continuirlichen Transformationsgruppen, insbesondere der Gruppen vom Range Null. Ph.D. Thesis, University of Leipzig, (1891), (In German). [32] Z. Yan and S. Deng, The classification of two step nilpotent complex Lie algebras of dimension 8, Czechoslovak Math. J., (3) 63 (2013), 847–863. | ||
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