Varieties of nilpotent Lie superalgebras of dimension ≤ 5

References

[1] M. A. Alvarez, The variety of 7-dimensional 2-step nilpotent Lie algebras, Symmetry 10 (2018), no. 1, Article ID 26. 10.3390/sym10010026Search in Google Scholar

[2] M. A. Alvarez and I. Hernández, On degenerations of Lie superalgebras, Linear Multilinear Algebra 68 (2020), no. 1, 29–44. 10.1080/03081087.2018.1498060Search in Google Scholar

[3] M. A. Alvarez, I. Hernández and I. Kaygorodov, Degenerations of Jordan superalgebras, Bull. Malays. Math. Sci. Soc. 42 (2019), no. 6, 3289–3301. 10.1007/s40840-018-0664-3Search in Google Scholar

[4] J. M. Ancochea Bermúdez, R. Campoamor-Stursberg, L. García Vergnolle and J. Sánchez Hernández, Contractions d’algèbres de Jordan en dimension 2, J. Algebra 319 (2008), no. 6, 2395–2409. 10.1016/j.jalgebra.2008.01.004Search in Google Scholar

[5] J. M. Ancochea Bermúdez, J. Fresán and J. Margalef Bentabol, Contractions of low-dimensional nilpotent Jordan algebras, Comm. Algebra 39 (2011), no. 3, 1139–1151. 10.1080/00927871003649393Search in Google Scholar

[6] A. Armour and Y. Zhang, Geometric classification of 4-dimensional superalgebras, Algebra, Geometry and Mathematical Physics, Springer Proc. Math. Stat. 85, Springer, Heidelberg (2014), 291–323. 10.1007/978-3-642-55361-5_18Search in Google Scholar

[7] A. Borel, Linear Algebraic Groups, 2nd ed., Grad. Texts in Math. 126, Springer, New York, 1991. 10.1007/978-1-4612-0941-6Search in Google Scholar

[8] D. Burde, Degenerations of nilpotent Lie algebras, J. Lie Theory 9 (1999), no. 1, 193–202. Search in Google Scholar

[9] D. Burde, Degenerations of 7-dimensional nilpotent Lie algebras, Comm. Algebra 33 (2005), no. 4, 1259–1277. 10.1081/AGB-200053956Search in Google Scholar

[10] D. Burde and C. Steinhoff, Classification of orbit closures of 4-dimensional complex Lie algebras, J. Algebra 214 (1999), no. 2, 729–739. 10.1006/jabr.1998.7714Search in Google Scholar

[11] R. Carles and Y. Diakité, Sur les variétés d’ algèbres de Lie de dimension  ≤7, J. Algebra 91 (1984), no. 1, 53–63. 10.1016/0021-8693(84)90125-XSearch in Google Scholar

[12] M. Couture, J. Patera, R. T. Sharp and P. Winternitz, Graded contractions of sl⁢(3,𝐂), J. Math. Phys. 32 (1991), no. 9, 2310–2318. 10.1063/1.529154Search in Google Scholar

[13] B. D. Craven, Complex symmetric matrices, J. Aust. Math. Soc. 10 (1969), 341–354. 10.1017/S1446788700007588Search in Google Scholar

[14] I. Gorshkov, I. Kaygorodov and Y. Popov, Degenerations of Jordan algebras, preprint (2017), https://arxiv.org/abs/1707.08836; to appear in Algebra Colloq.. Search in Google Scholar

[15] A. Fialowski and M. Penkava, Moduli spaces of low dimensional Lie superalgebras, preprint (2017), https://arxiv.org/abs/1709.00764. 10.1142/S0129167X21500592Search in Google Scholar

[16] J. R. Gómez, Y. Khakimdjanov and R. M. Navarro, Some problems concerning to nilpotent Lie superalgebras, J. Geom. Phys. 51 (2004), no. 4, 473–486. 10.1016/j.geomphys.2004.01.003Search in Google Scholar

[17] F. Grunewald and J. O’Halloran, Varieties of nilpotent Lie algebras of dimension less than six, J. Algebra 112 (1988), no. 2, 315–325. 10.1016/0021-8693(88)90093-2Search in Google Scholar

[18] A. Hegazi, Classification of nilpotent Lie superalgebras of dimension five. I, Internat. J. Theoret. Phys. 38 (1999), no. 6, 1735–1739. 10.1023/A:1026663115571Search in Google Scholar

[19] I. Hernández, G. Salgado and O. A. Sánchez-Valenzuela, Lie superalgebras based on a 3-dimensional real or complex Lie algebra, J. Lie Theory 16 (2006), no. 3, 539–560. Search in Google Scholar

[20] J. F. Herrera-Granada and P. Tirao, The Grunewald–O’Halloran conjecture for nilpotent Lie algebras of rank  ≥1, Comm. Algebra 44 (2016), no. 5, 2180–2192. 10.1080/00927872.2015.1044097Search in Google Scholar

[21] J. Hrivnák, P. Novotný, J. Patera and J. Tolar, Graded contractions of the Pauli graded sl⁢(3,ℂ), Linear Algebra Appl. 418 (2006), no. 2–3, 498–550. 10.1016/j.laa.2006.02.026Search in Google Scholar

[22] I. Kashuba and M. E. Martin, Deformations of Jordan algebras of dimension four, J. Algebra 399 (2014), 277–289. 10.1016/j.jalgebra.2013.09.040Search in Google Scholar

[23] I. Kashuba and J. Patera, Graded contractions of Jordan algebras and of their representations, J. Phys. A 36 (2003), no. 50, 12453–12473. 10.1088/0305-4470/36/50/006Search in Google Scholar

[24] A. A. Kirillov and Y. A. Neretin, The Variety An of n-dimensional Lie algebra structures, Amer. Math. Soc. Transl. 137 (1987), no. 2, 21–30. 10.1090/trans2/137/03Search in Google Scholar

[25] J. Lauret, Degenerations of Lie algebras and geometry of Lie groups, Differential Geom. Appl. 18 (2003), no. 2, 177–194. 10.1016/S0926-2245(02)00146-8Search in Google Scholar

[26] N.-L. Matiadou and A. Fellouris, A classification of the five-dimensional Lie superalgebras, over the complex numbers, Math. Balkanica (N. S.) 19 (2005), no. 1–2, 143–154. Search in Google Scholar

[27] D. Mumford, The Red Book of Varieties and Schemes, Lecture Notes in Math. 1358, Springer, Berlin, 1988. 10.1007/978-3-662-21581-4Search in Google Scholar

[28] M. Nesterenko and R. Popovych, Contractions of low-dimensional Lie algebras, J. Math. Phys. 47 (2006), no. 12, Article ID 123515. 10.1063/1.2400834Search in Google Scholar

[29] M. Scheunert, The Theory of Lie Superalgebras. An Introduction, Lecture Notes in Math. 716, Springer, Berlin, 1979. 10.1007/BFb0070929Search in Google Scholar

[30] C. Seeley, Degenerations of 6-dimensional nilpotent Lie algebras over 𝐂, Comm. Algebra 18 (1990), no. 10, 3493–3505. 10.1080/00927879008824088Search in Google Scholar

[31] P. Tirao and S. Vera, There are no rigid filiform Lie algebras of low dimension, J. Lie Theory 29 (2019), no. 2, 391–412. Search in Google Scholar

[32] E. Weimar-Woods, The three-dimensional real Lie algebras and their contractions, J. Math. Phys. 32 (1991), no. 8, 2028–2033. 10.1063/1.529222Search in Google Scholar

[33] K. Zheng and Y. Zhang, On (α,β,γ)-derivations of Lie superalgebras, Int. J. Geom. Methods Mod. Phys. 10 (2013), no. 10, Article ID 1350050. 10.1142/S0219887813500503Search in Google Scholar