On analogs of some group-theoretic concepts and results for Leibniz algebras

1Kurdachenko, LA, 2Subbotin, IYa., 3Semko, NN
1Oles Honchar Dnipropetrovsk National University
2National University, Los Angeles, USA
3State Tax Service National University of Ukraine, Irpin
Dopov. Nac. akad. nauk Ukr. 2018, 1:10-14
Section: Mathematics
Language: English

An algebra L over a field F is said to be a Leibniz algebra (more precisely a left Leibniz algebra) if it satisfies the Leibniz identity: [[a, b], c] = [a, [b, c]] – [b, [a, c]] for all a, b, c ∈ L. Leibniz algebras are generalizations of Lie algebras. We consider some classes of generalized nilpotent Leibniz algebras (hypercentral, locally nilpotent algebras, and algebras with the idealizer condition) and show their some basic properties.

Keywords: ascendant subalgebra, center of a Leibniz algebra, hypercentral Leibniz algebra, ideal, idealizer condition, left center, Leibniz algebra, Leibniz algebra with the idealizer condition, Lie algebra, locally nilpotent Leibniz algebra, right center
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