Vladimir V. Kirichenko, Leonid A. Kurdachenko, Aleksandr A. Pypka, Igor Ya. Subbotin, “Some aspects of Leibniz algebra theory”, Algebra Discrete Math., 2017, Volume 24, Issue 1,Pages <nobr>1

This article is cited in 7 papers

SURVEY ARTICLE

Some aspects of Leibniz algebra theory

Vladimir V. Kirichenko^a, Leonid A. Kurdachenko^b, Aleksandr A. Pypka^b, Igor Ya. Subbotin^c

^a Faculty of Mechanics and Mathematics, Taras Shevchenko National University of Kyiv, Volodymyrska str., 64, Kyiv, 01033, Ukraine
^b Department of Geometry and Algebra, Faculty of Mechanics and Mathematics, Oles Honchar Dniprovsk National University, Gagarin ave., 72, Dnipro, 49010, Ukraine
^c Department of Mathematics and Natural Sciences, College of Letters and Sciences, National University, 5245 Pacific Concourse Drive, LA, CA 90045, USA

Abstract: One of the key tendencies in the development of Leibniz algebra theory is the search for analogues of the basic results of Lie algebra theory. In this survey, we consider the reverse situation. Here the main attention is paid to the results reflecting the difference of the Leibniz algebras from the Lie algebras.

Keywords: Leibniz algebra, cyclic Leibniz algebra, left (right) center, lower (upper) central series, finite dimensional Leibniz algebra, nilpotent Leibniz algebra, extraspecial Leibniz algebra, bilinear form, left (right) idealizer, Frattini subalgebra, nil-radical, nil-algebra, soluble Leibniz algebra, left (right) subideal, Leibniz $T$-algebra, Baer radical.

MSC: 17A32, 17A60

Received: 02.06.2017

Language: English