References

  1. Ayupov S.A., Omirov B.A. On 3-dimensional Leibniz algebras. Uzbek Math. J. 1999, 1, 9-14.
  2. Albeverio S., Omirov B.A., Rakhimov I.S. Varieties of nilpotent complex Leibniz algebras of dimension less than five. Comm. Algebra 2005, 33 (5), 1575-1585. doi: 10.1081/AGB-200061038
  3. Baer R. Situation der Untergruppen und Struktur der Gruppe. S.-B. Heidelberg Acad. Math.-Nat. Klasse 1933, 2, 12-17.
  4. Baer R. Endlichkeitskriterien für Kommutatorgruppen. Math. Ann. 1952, 124 (1), 161-177. doi: 10.1007/BF01343558
  5. Bloh A.M. On a generalization of the concept of Lie algebra. Dokl. Akad. Nauk SSSR 1965, 165 (3), 471-473. (in Russian)
  6. Bloh A.M. Cartan-Eilenberg homology theory for a generalized class of Lie algebras. Dokl. Akad. Nauk SSSR 1967, 175 (8), 824-826. (in Russian)
  7. Bloh A.M. A certain generalization of the concept of Lie algebra. Algebra and number theory. Moskov. Gos. Ped. Inst. Uchen. Zap. 1971, 375, 9-20.
  8. Butterfield J., Pagonis C. From Physics to Philosophy. Cambridge Univ. Press, Cambridge, 1999.
  9. Casas J.M., Insua M.A., Ladra M., Ladra S. An algorithm for the classification of 3-dimensional complex Leibniz algebras. Linear Algebra Appl. 2012, 436 (9), 3747-3756. doi: 10.1016/j.laa.2011.11.039
  10. Chupordia V.A., Kurdachenko L.A., Subbotin I. Ya. On some ''minimal'' Leibniz algebras. J. Algebra Appl. 2017, 16 (05), 1750082 (16 pages). doi: 10.1142/S0219498817500827
  11. Demir I., Misra K.C., Stitzinger E. On some structures of Leibniz algebras. Recent Advances in Representation Theory, Quantum Groups, Algebraic Geometry, and Related Topics, Contemporary Mathematics 2014, 623, 41-54. doi: 10.1090/conm623/12456
  12. Dobrev V. Lie Theory and its applications in physic. IX International workshop. Springer, Tokyo, 2013.
  13. Duplij S., Wess J. Noncommutative Structures in Mathematics and Physics, Proceedings of the NATO advanced research workshop. Springer, Kiev, 2001.
  14. Farnsteiner R. On the structure of simple-semiabelian Lie algebras. Pacific J. Math. 1984, 111, 287-299. doi: 10.2140/pjm.1984.111.287
  15. Gejn A.G. Minimal noncommutative and minimal nonabelian algebras. Comm. Algebra 1985, 13, 305-328. doi: 10.1080/00927878508823161
  16. Gejn A.G., Kuznetsov S.V., Mukhin Yu.N. On minimal non-nilpotent Lie algebras. Ural. Gos. Univ. Mat. Zap. 1972, 8, 18-27.
  17. Gejn A., Mukhin Yu.N. Complements to subalgebras of Lie algebras. Ural. Gos. Univ. Mat. Zap. 1980 12 (2), 24-48.
  18. Kirichenko V.V., Kurdachenko L.A., Pypka A.A., Subbotin I.Ya. Some aspects of Leibniz algebra theory. Algebra Discrete Math. 2017 24 (1), 1-33.
  19. Kurdachenko L.A., Otal J., Pypka A.A. Relationships between factors of canonical central series of Leibniz algebras. Eur. J. Math. 2016, 2 (2), 565-577. doi: 10.1007/s40879-016-0093-5
  20. Kurdachenko L.A., Semko N.N., Subbotin I.Ya. The Leibniz algebras whose subalgebras are ideals. Open Math. 2017, 15 (1), 92-100. doi: 10.1515/math-2017-0010
  21. Kurdachenko L.A., Semko N.N., Subbotin I.Ya. On the anticommutativity in Leibniz algebras. Algebra Discrete Math. 2018 26 (1), 97-109.
  22. Kurdachenko L.A., Subbotin I.Y., Semko N.N. From Groups to Leibniz Algebras: Common Approaches, Parallel Results. Adv. Group Theory Appl. 2018 5, 1-31. doi: 10.4399/97888255161421
  23. Kurdachenko L.A., Subbotin I.Ya., Yashchuk V.S. On Some Antipodes of the Ideals in Leibniz Algebras. J. Algebra Appl. 2019. doi: 10.1142/S0219498820501133
  24. Kurdachenko L.A., Subbotin I.Ya., Yashchuk V.S. Leibniz Algebras Whose Subideals are Ideals. J. Algebra Appl. 2018, 17 (08) 1850151. doi: 10.1142/S0219498818501517
  25. Loday J.-L. Une version non commutative des algèbres de Lie: les algèbras de Leibniz. Enseign. Math. 1993, 39, 269-293.
  26. Loday J.-L. Cyclic homology. Grundlehren Math. Wiss. Vol. 301, 2nd ed., Springer, Verlag, Berlin, 1998.
  27. Neumann B.H. Groups with finite classes of conjugate elements. Proc. Lond. Math. Soc. 1951, 3 (1), 178-187. doi: 10.1112/plms/s3-1.1.178
  28. Stewart I.N. Subideals of Lie algebras. Ph.D. Thesis, University of Warwick. 1969.
  29. Stewart I.N. Verbal and marginal properties of non-associative algebras in the spirit of infinite group theory. Proc. Lond. Math. Soc. 1974, 3 (28), 129-140. doi: 10.1112/plms/s3-28.1.129
  30. Stitzinger E.L. Minimal nonnilpotent solvable Lie algebras. Proc. Amer. Math. Soc. 1971, 28, 47-49. doi: 10.1090/S0002-9939-1971-0271178-X
  31. Towers D.A. Lie algebras all whose proper subalgebras are nilpotent. Linear Algebra Appl. 1980, 32, 61-73. doi: 10.1016/0024-3795(80)90007-5
  32. Vaughan-Lee M.R. Metabelian BFC p-groups. J. Lond. Math. Soc. 1972, 5 (4), 673-680. doi: 10.1112/jlms/s2-5.4.673
  33. Yashchuk V.S. On some Leibniz algebras, having small dimension. Algebra Discrete Math. 2019, 27 (2), 292-308.