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Communications in Algebra Volume 51, 2023 - Issue 9
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Research Articles

Second-maximal subalgebras of Leibniz algebras

Lindsey Bosko-Dunbara Mathematics Discipline, St. Norbert College, De Pere, Wisconsin, USA
,
Jonathan D. Dunbara Mathematics Discipline, St. Norbert College, De Pere, Wisconsin, USA
,
J. T. Hirdb Department of Mathematics, West Virginia University, Institute of Technology, Montgomery, West Virginia, USACorrespondence[email protected]
&
Kristen Stagg Rovirac Department of Mathematics, California State University, Dominguez Hills, Carson, California, USA
Pages 3965-3971 | Received 12 Sep 2022, Accepted 14 Mar 2023, Published online: 29 Mar 2023

References

  • Albeverio, S., Omirov, B. A., Rakhimov, I. S. (2006). Classification of 4 dimensional nilpotent complex Leibniz algebras. Extracta Math. 21(3):197–210.
  • Ayupov, Sh. A., Omirov, B. A. (1998). On Leibniz algebras. Algebra and Operator Theory. Proceedings of the Colloquium in Tashkent, Kluwer.
  • Barnes, D. (2012). On Levi’s theorem for Leibniz algebras. Bull. Austral. Math. Soc. 86(2):184–185. DOI: 10.1017/S0004972711002954.
  • Batten, C., Bosko-Dunbar, L., Hedges, A., Hird, J. T., Stagg, K., Stitzinger, E. (2013). A Frattini theory for Leibniz algebras. Commun. Algebra. 41(4):1547–1557.
  • Bloh, A. (1965). On a generalization of Lie algebra notion. Math. USSR Doklady 165:471–473.
  • Bonezzi, R., Hohm, O. (2020). Leibniz Guage theories and infinity structures. Commun. Math. Phys. 377:2027–2077.
  • Bosko-Dunbar, L., Dunbar, J., Hird, J. T., Stagg, K. (2015). Solvable Leibniz algebras with Heisenberg nilradical. Commun. Algebra 43(6):2272–2281.
  • Bosko-Dunbar, L., Dunbar, J., Hird, J. T., Stagg, K. (2020). Minimal nonnilpotent Leibniz algebras. IEJA 28:187–192.
  • Cañete, E. M., Khudoyberdiyev, A. K. (2013). The classification of 4-dimensional Leibniz algebras. Linear Algebra Appl. 439(1):273–288.
  • Casas, J. M., Ladra, M., Omirov, B. A., Karimjanov, I. A. (2013). Classification of solvable Leibniz algebras with null-filiform nilradical. Linear Multilinear Algebra 61(6):758–774.
  • Casas, J. M., Ladra, M., Omirov, B. A., Karimjanov, I. A. (2013). Classification of solvable Leibniz algebras with naturally graded filiform nil-radical. Linear Algebra Appl. 438(7):2973–3000.
  • Demir, I., Misra, K., Stitzinger, E. On some structures of Leibniz algebras. arxiv:1307.7672.
  • Dynkin, E. B. (1947). The structure of semi-simple algebras. Uspekhi Mat. Nauk, N.S. 2(4(20)):59–127 (in Russian).
  • Kurdachenko, L., Semko, N., Subbotin, I. (2017). The Leibniz algebras whose subalgebras are ideals. Open Math 15(1):92–100.
  • Loday, J. (1993). Une version non commutative des algebres de Lie: les algebres de Leibniz. Enseign. Math. 39: 269–293.
  • Loday, J., Pirashvili, T. (1993). Universal enveloping algebras of Leibniz algebras and (co)homology. Math. Ann. 296:139–158.
  • McAlister, A., Stagg Rovira, K., Stitzinger, E. (2019). Frattini properties and nilpotency in Leibniz algebras. IEJA 25:64–76.
  • Omirov, B. (2006). Conjugacy of Cartan subalgebras of complex finite dimensional Leibniz algebras. J. Algebra. 302:887–896.
  • Rikhsiboev, I., Rakhimov, I. (2012). Classification of three dimensional complex Leibniz algebras. AIP Conf. Proc. 1450:358. DOI: 10.1063/1.4724168.
  • Stitzinger, E. (1970). A note on a class of Lie algebras. Math Z. 116:141–142.

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