Leibniz algebras: a brief review of current results

Authors

  • V.A. Chupordia Oles Honchar Dnipro National University, 72 Gagarin avenue, 49010, Dnipro, Ukraine
  • A.A. Pypka Oles Honchar Dnipro National University, 72 Gagarin avenue, 49010, Dnipro, Ukraine https://orcid.org/0000-0003-0837-5395
  • N.N. Semko University of the State Fiscal Service of Ukraine, 31 Universitetskaya str., 08205, Irpin, Ukraine https://orcid.org/0000-0003-0123-4872
  • V.S. Yashchuk Oles Honchar Dnipro National University, 72 Gagarin avenue, 49010, Dnipro, Ukraine
https://doi.org/10.15330/cmp.11.2.250-257

Keywords:

Leibniz algebra, cyclic Leibniz algebra, ideal, subideal, contraideal, center, lower (upper) central series, finite-dimensional Leibniz algebra, nilpotent Leibniz algebra, Leibniz T-algebra, anticenter, antinilpotent Leibniz algebra
Published online: 2019-12-31

Abstract

Let L be an algebra over a field F with the binary operations + and [⋅,⋅]. Then L is called a left Leibniz algebra if it satisfies the left Leibniz identity [[a,b],c]=[a,[b,c]]−[b,[a,c]] for all a,b,c∈L. This paper is a brief review of some current results, which related to finite-dimensional and infinite-dimensional Leibniz algebras.

Article metrics
How to Cite
(1)
Chupordia, V.; Pypka, A.; Semko, N.; Yashchuk, V. Leibniz Algebras: A Brief Review of Current Results. Carpathian Math. Publ. 2019, 11, 250-257.