On some "minimal" Leibniz algebras

1Kurdachenko, LA, 2Subbotin, IYa., 1Chupordia, VA
1Oles Honchar Dnipropetrovsk National University
2National University, Los Angeles, USA
Dopov. Nac. akad. nauk Ukr. 2016, 11:5-9
https://doi.org/10.15407/dopovidi2016.11.005
Section: Mathematics
Language: Ukrainian
Abstract: 

The description of the Leibniz algebras, whose proper subalgebras are Lie algebras, and the Leibniz algebras, whose
proper subalgebras are Abelian, is obtained.

Keywords: cyclic algebra, Leibniz algebra, Lie algebra
References: 
  1. Bloh A.M. Soviet Math. Dokl., 1965, 6: 1450—1452.
  2. Bloh A.M. Soviet Math. Dokl., 1967, 8: 824—826.
  3. Bloh A.M. Algebra and number theory. Uchenye Zapiski Moskov. Gos. Pedagog. Inst., 1971, 375: 9—20 (in Russian).
  4. Loday J.L. Enseign. Math, 1993, 39: 269—293.
  5. Loday J.L., Pirashvili T. Math. Ann., 1993, 296: 139—158. doi: https://doi.org/10.1007/BF01445099
  6. Frabetti A. J. Pure Appl. Algebra, 1998, 129: 123—141. doi: https://doi.org/10.1016/S0022-4049(97)00066-2
  7. Casas J.M., Pirashvili T. J. Algebra, 2000, 231: 258—264. doi: https://doi.org/10.1006/jabr.1999.8364
  8. Kurdachenko L.A., Otal J., Pypka A.A. European Journal of Mathematics, 2016, 2: 565. doi: https://doi.org/10.1007/s40879-016-0093-5
  9. Stitzinger E.L. Proc. Amer. Math. Soc., 1971, 28: 47—49. doi: https://doi.org/10.1090/S0002-9939-1971-0271178-X
  10. Gein A.G., Kuznetsov S.V., Mukhin Yu.N. Mat. Zapiski Uralsk. Gos. Univ., 1972, 8, No 3: 18—27 (in Russian).
  11. Towers D.A. Lin. Algebra Appl., 1980, 32: 61—73. doi: https://doi.org/10.1016/0024-3795(80)90007-5
  12. Farnsteiner R. Pacific J. Math., 1984, 111: 287—299. doi: https://doi.org/10.2140/pjm.1984.111.287
  13. Gein A.G. Commun. Algebra, 1985, 13: 305—328. doi: https://doi.org/10.1080/00927878508823161