Degenerations of binary Lie and nilpotent Malcev algebras

References

• Ancochea Bermúdez, J. M., Campoamor-Stursberg, R., García Vergnolle, L., Sánchez Hernández, J. (2008). Contractions d´algebres de Jordan en dimension 2. J. Algebra 319(6):2395–2409.
   Web of Science ®Google Scholar
• Benes, T., Burde, D. (2009). Degenerations of pre-Lie algebras. J. Math. Phys. 50(11): 112102.
   Web of Science ®Google Scholar
• Benes, T., Burde, D. (2014). Classification of orbit closures in the variety of three-dimensional Novikov algebras. J. Algebra Appl. 13(2): 1350081.
   Google Scholar
• Burde, D. (1999). Degenerations of nilpotent Lie algebras. J. Lie Theory 9(1):193–202.
   Web of Science ®Google Scholar
• Burde, D. (2003). Sur les degenerations d’algebres de Lie. https://homepage.univie.ac.at/Dietrich.Burde/papers/burde_15_rapp_deg.pdf.
   Google Scholar
• Burde, D. (2005). Degenerations of 7-dimensional nilpotent Lie algebras. Commun. Algebra 33(4):1259–1277.
   Web of Science ®Google Scholar
• Burde, D., Steinhoff, C. (1999). Classification of orbit closures of 4–dimensional complex Lie algebras. J. Algebra 214(2):729–739.
   Web of Science ®Google Scholar
• Casas, J., Khudoyberdiyev, A., Ladra, M., Omirov, B. (2013). On the degenerations of solvable Leibniz algebras. Linear Algebra Appl. 439(2):472–487.
   Web of Science ®Google Scholar
• Chouhy, S. On geometric degenerations and Gerstenhaber formal deformations. ArXiv:1708.02933.
   Google Scholar
• Filippov, V. (2000). On δ-derivations of prime alternative and Malcev algebras. Algebra Logic 39(5):618–625.
   Google Scholar
• Gabriel, P. (1975). Finite representation type is open. In: Proceedings of the International Conference on Representations of Algebras, Carleton University, Ottawa, Ontario, 1974. Lecture Notes in Mathematics, Vol. 488, pp. 132–155.
   Google Scholar
• Gainov, A. (1957). Identical relations for binary Lie rings (Russian). Uspehi Mat. Nauk N.S. 12(3(75)):141–146.
   Google Scholar
• Gainov, A. (1963). Binary Lie algebras of lower ranks (Russian). Algebra i Logika Sem. 2(4):21–40.
   Google Scholar
• Gorbatsevich, V. (1994). Anticommutative finite-dimensional algebras of the first three levels of complexity. St. Petersburg Math. J. 5(3):505–521.
   Google Scholar
• Gorshkov, I., Kaygorodov, I., Popov, Y. Degenerations of Jordan algebras. ArXiv:1707.08836.
   Google Scholar
• Grunewald, F., O’Halloran, J. (1988). A characterization of orbit closure and applications. J. Algebra 116:163–175.
   Web of Science ®Google Scholar
• Grunewald, F., O’Halloran, J. (1988). Varieties of nilpotent Lie algebras of dimension less than six. J. Algebra 112: 315–325.
   Web of Science ®Google Scholar
• Ismailov, N., Kaygorodov, I., Volkov, Y. (2018). The geometric classification of Leibniz algebras. Int. J. Math., 29. doi: 10.1142/S0129167X18500350.
   Google Scholar
• Kaygorodov, I. (2014). On (n+1)-ary derivations of simple n-ary Malcev algebras. St. Petersburg Math. J. 25(4): 575–585.
   Web of Science ®Google Scholar
• Kaygorodov, I., Popov, Y. (2016). A characterization of nilpotent nonassociative algebras by invertible Leibniz-derivations. J. Algebra 456:323–347.
   Web of Science ®Google Scholar
• Kaygorodov, I., Popov, Y., Pozhidaev, A., Volkov, Y. (2018). Degenerations of Zinbiel and nilpotent Leibniz algebras. Linear Multilinear Algebra 66(4):704–716.
   Web of Science ®Google Scholar
• Kaygorodov, I., Volkov, Y. The variety of 2-dimensional algebras over an algebraically closed field. ArXiv:1701.08233.
   Google Scholar
• Khudoyberdiyev, A. (2015). The classification of algebras of level two. J. Geom. Phys. 98:13–20.
   Web of Science ®Google Scholar
• Khudoyberdiyev, A., Omirov, B. (2013). The classification of algebras of level one. Linear Algebra Appl. 439(11): 3460–3463.
   Web of Science ®Google Scholar
• Kuzmin, E. (1970). Malcev algebras of dimension five over a field of characteristic zero. Algebra Logic 9:416–421.
   Google Scholar
• Kuzmin, E. (1971). The connection between Malcev algebras and analytic Moufang loops. Algebra Logic 10:3–22.
   Google Scholar
• Kuzmin, E. (1998). Binary Lie algebras of small dimension. Algebra Logic 37(3):181–186.
   Google Scholar
• Kuzmin, E. (2014). Structure and representations of finite dimensional Malcev algebras. Quasigroups Relat. Syst. 22(1):97–132.
   Google Scholar
• Lauret, J. (2003). Degenerations of Lie algebras and geometry of Lie groups. Differ. Geom. Appl. 18(2):177–194.
   Web of Science ®Google Scholar
• Malcev, A. (1955). Analytic loops (Russian). Mat. Sb. N.S. 36:569–576.
   Google Scholar
• Mazzola, G. (1979). The algebraic and geometric classification of associative algebras of dimension five. Manuscripta Math. 27:81–101.
   Web of Science ®Google Scholar
• Mazzola, G. (1980). Generic finite schemes and Hochschild cocycles. Comment. Math. Helv. 55:267–293.
   Web of Science ®Google Scholar
• Pozhidaev, A. (2001). n-ary Malcev algebras. Algebra Logic 40(3):170–182.
   Google Scholar
• Sagle, A. (1961). Malcev algebras. Trans. Am. Math. Soc. 101:426–458.
   Google Scholar
• Seeley, C. (1990). Degenerations of 6-dimensional nilpotent Lie algebras over ℂ. Commun. Algebra 18:3493–3505.
   Web of Science ®Google Scholar