### Methods of group theory in Leibniz algebras: some compelling results

#### Abstract

#### Keywords

#### Full Text:

PDF#### References

Amayo R.K., Stewart I. *Infinite Dimensional Lie Algebras*, Noordhoff Int. Publ., 1974.

Ayupov Sh.A., Omirov B.A., Rakhimov I.S. *Leibniz Algebras: Structure and Classification*, CRC Press, Taylor&Francis Group, 2020.

Blokh A. "On a generalization of the concept of Lie algebra", *Dokl. Akad. nauk USSR*, 1965; 165: 471-473. (in Russian)

Barnes D. "Schunck classes of soluble Leibniz algebras", *Comm. Algebra*, 2013; 41: 4046-4065. doi:10.1080/00927872.2012.700978

Chupordya V.A., Kurdachenko L.A., Subbotin I.Ya. "On some 'minimal' Leibniz algebras", *J. Algebra Appl.*, 2017; 16: 1750082. doi:10.1142/S0219498817500827

Chupordya V.A., Kurdachenko L.A., Semko N.N. "On the structure of Leibniz algebras whose subalgebras are ideals or core-free", *Algebra Discrete Math.*, 2020; 29: pp. 180-194. doi:10.12958/adm1533

Hartley B. "Locally nilpotent ideals of a Lie algebra", *Math. Proc. Cambridge Philos. Soc.*, 1967; 63: pp. 257-272. doi:10.1017/S0305004100041177

Hirsch K.A. "Über lokal-nilpotente Gruppen", *Math. Z.*, 1955; 63: pp. 290-291. doi:10.1007/BF01187939

Kurdachenko L.A., Semko N.N., Subbotin I.Ya. "The Leibniz algebras whose subalgebras are ideals", *Open Math.*, 2017; 15: pp. 92-100. doi:10.1515/math-2017-0010

Kurdachenko L.A., Subbotin I.Ya., Semko N.N. "On the anticommutativity in Leibniz algebras", *Algebra Discrete Math.*, 2018; 26: pp. 97-109.

Kurdachenko L.A., Subbotin I.Ya., Semko N.N. "From groups to Leibniz algebras: common approaches, parallel results", *Adv. Group Theory Appl.*, 2018; 5: pp. 1-31. doi:10.4399/97888255161421

Kurdachenko L.A., Subbotin I.Ya., Yashchuk V.S. "The Leibniz algebras whose subideals are ideals", *J. Algebra Appl.*, 2018; 17: 1850151. doi:10.1142/S0219498818501517

Kurdachenko L.A., Subbotin I.Ya., Yashchuk V.S. "On ideals and contraideals in Leibniz algebras", *Dopov. Nac. akad. nauk Ukr.*, 2020; 1: pp. 11-15. doi:10.15407/dopovidi2020.01.011

Kurdachenko L.A., Subbotin I.Ya., Yashchuk V.S. "Some antipodes of ideals in Leibniz algebras", *J. Algebra Appl.*, 2020; 19: 2050113. doi:10.1142/S0219498820501133

Kurdachenko L.A., Subbotin I.Ya., Yashchuk V.S. "Leibniz algebras whose subalgebras are left ideals", *Serdica Math. J.*, 2020; 46: pp. 175-194.

Kurdachenko L.A., Otal J., Pypka A.A. "Relationships between factors of canonical central series of Leibniz algebras", *Eur. J. Math.*, 2016; 2: pp. 565-577. doi:10.1007/s40879-016-0093-5

Kurdachenko L.A., Otal J., Subbotin I.Ya. "On some properties of the upper central series in Leibniz algebras", *Comment. Math. Univ. Carolin.*, 2019; 60: pp. 161-175. doi:10.14712/1213-7243.2019.009

Loday J.L. "Une version non commutative des algèbres de Lie: les algèbres de Leibniz", *Enseign. Math.*, 1993; 39: pp. 269-293. (in French)

Loday J.L., Pirashvili T. "Universal enveloping algebras of Leibniz algebras and (co)homology", *Math. Ann.*, 1993; 296: pp. 139-158.

Maltsev A.I. "Nilpotent torsion-free groups", *Izv. Akad. nauk USSR*, 1949; 13: pp. 201-212. (in Russian)

Plotkin B.I. "To the theory of locally nilpotent groups", *Dokl. Akad. nauk USSR*, 1951; 76: pp. 655--657. (in Russian)

Plotkin B.I. "Radical groups", *Mat. sbornik*, 1955; 37: pp. 507-526. (in Russian)

Plotkin B.I. "Generalized soluble and generalized nilpotent groups", *Uspekhi. Mat. Nauk*, 1958; 13: pp. 89-172. (in Russian)

Scofield D., McKay Sullivan S. "Classification of complex cyclic Leibniz algebras", 2014; arXiv:1411.0170v2

DOI: https://doi.org/10.15421/242108

### Refbacks

- There are currently no refbacks.

Copyright (c) 2021 I.Ya. Subbotin

This work is licensed under a Creative Commons Attribution 4.0 International License.