Central extensions of 2-filiform Leibniz algebras

References

• Adashev, J., Camacho, L., Omirov, B. (2017). Central extensions of null-filiform and naturally graded filiform non-Lie Leibniz algebras. J. Algebra. 479:461–486. DOI: 10.1016/j.jalgebra.2017.02.003.
   Web of Science ®Google Scholar
• Ayupov, Sh. A., Omirov, B. A. (2001). On some classes of nilpotent Leibniz algebras. Siberian Math. J. 42(1):15–24. DOI: 10.1023/A:1004829123402.
   Web of Science ®Google Scholar
• Albeverio, S., Ayupov, Sh. A., Omirov, B. A. (2005). On nilpotent and simple Leibniz algebras. Commun. Algebra. 33(1):159–172. DOI: 10.1081/AGB-200040932.
   Web of Science ®Google Scholar
• Albeverio, S., Omirov, B. A., Rakhimov, I. S. (2006). Classification of 4-dimensional nilpotent complex Leibniz algebras. Extract. Math. 21(3):197–210.
   Google Scholar
• Bäuerle, G. G. A., de Kerf, E. A., ten Kroode, A. P. E. (1997). Lie algebras. Part 2. Finite and infinite dimensional Lie algebras and applications in physics. In: de Jager, E. M., ed. Studies in Mathematical Physics, vol. 7. Amsterdam: North-Holland Publishing Co., pp. x+554.
   Google Scholar
• Cahen, M., Ohn, C. (1989). Bialgebra structures on the Heisenberg algebra. Bulletin de la Classe des Sciencies de L’Academia Royale de Belgique 75:315–321. DOI: 10.3406/barb.1989.57848.
   Google Scholar
• Cicalò, S., De Graaf, W., Schneider, C. (2012). Six-dimensional nilpotent Lie algebras. Linear Algebra Appl. 436(1):163–189. DOI: 10.1016/j.laa.2011.06.037.
   Web of Science ®Google Scholar
• Camacho, L. M., Gómez, J. R., Gónzalez, A. J., Omirov, B. A. (2009). Naturally graded quasi-filiform Leibniz algebras. J. Symbol. Comput. 44(5):527–539. DOI: 10.1016/j.jsc.2008.01.006.
   Web of Science ®Google Scholar
• Camacho, L. M., Gómez, J. R., González, A. J., Omirov, B. A. (2010). Naturally graded 2-filiform Leibniz algebras. Commun. Algebra. 38(10):3671–3685. DOI: 10.1080/00927870903236160.
   Web of Science ®Google Scholar
• Camacho, L. M., Gómez, J. R., González, A. J., Omirov, B. A. (2011). The classification of naturally graded p-filiform Leibniz algebras. Commun. Algebra. 39(1):153–168. DOI: 10.1080/00927870903451900.
   Web of Science ®Google Scholar
• Camacho, L. M., Karimjanov, I., Kaygorodov, I., Khudoyberdiyev, A. (2022). Central extensions of filiform Zinbiel algebras. Linear Multilinear Algebra. 70(8):1479–1495. DOI: 10.1080/03081087.2020.1764903.
   Web of Science ®Google Scholar
• Gómez, J. R., Omirov, B. A. (2015). On classification of complex filiform Leibniz algebras. Algebra Colloq., 22(1):757–774. DOI: 10.1142/S1005386715000668.
   Web of Science ®Google Scholar
• Darijani, I., Usefi, H. (2016). The classification of 5-dimensional p-nilpotent restricted Lie algebras over perfect fields, I. J. Algebra 464:97–140. DOI: 10.1016/j.jalgebra.2016.06.011.
   Web of Science ®Google Scholar
• De Graaf, W. (2007). Classification of 6-dimensional nilpotent Lie algebras over fields of characteristic not 2. J. Algebra. 309(2):640–653. DOI: 10.1016/j.jalgebra.2006.08.006.
   Web of Science ®Google Scholar
• Demir, I. (2016). Classification of 5-dimensional complex nilpotent Leibniz algebras. In: Representations of Lie Algebras, Quantum Groups and Related Topics. Contemporary Mathematics, 713, Raleigh, NC, pp. 95–120.
   Google Scholar
• Hegazi, A., Abdelwahab, H. (2018). The classification of n-dimensional non-associative Jordan algebras with (n−3)-dimensional annihilator. Commun. Algebra. 46(2):629–643. DOI: 10.1080/00927872.2017.1327052.
   Web of Science ®Google Scholar
• Hegazi, A., Abdelwahab, H., Calderón Martín, A. (2016). The classification of n-dimensional non-Lie Malcev algebras with (n−4)-dimensional annihilator. Linear Algebra Appl. 505:32–56. DOI: 10.1016/j.laa.2016.04.029.
   Web of Science ®Google Scholar
• Karimjanov, I., Kaygorodov, I., Ladra, M. (2021). Central extensions of filiform associative algebras. Linear Multilinear Algebra. 69(6):1083–1101. DOI: 10.1080/03081087.2019.1620674.
   Web of Science ®Google Scholar
• Loday, J. L. (1995). Cup product for Leibniz cohomology and dual Leibniz algebras. Math. Scand. 77:189–196. DOI: 10.7146/math.scand.a-12560.
   Web of Science ®Google Scholar
• Kaygorodov, I., Lopes, S., Páez-Guillán, P. (2020). Non-associative central extensions of null-filiform associative algebras. J. Algebra. 560:1190–1210. DOI: 10.1016/j.jalgebra.2020.06.013.
   Web of Science ®Google Scholar
• Skjelbred, T., Sund, T. (1978). Sur la classification des algebres de Lie nilpotentes. C. R. Acad. Sci. Paris Ser. A-B 286(5):A241–A242.
   Google Scholar
• Szymczak, I., Zakrzewski, S. (1990). Quantum deformation of the Heisenberg group obtained by geormetric quantization. J. Geometry Phys. 7(4):553–569. DOI: 10.1016/0393-0440(90)90006-O.
   Google Scholar
• Rakhimov, I., Hassan, M. (2011). On one-dimensional Leibniz central extensions of a filiform Lie algebra. Bull. Aust. Math. Soc. 84(2):205–224. DOI: 10.1017/S0004972711002371.
   Web of Science ®Google Scholar
• Zusmanovich, P. (1992). Central extensions of current algebras. Trans. Amer. Math. Soc. 334(1):143–152. DOI: 10.2307/2153976.
   Web of Science ®Google Scholar