On analogs of some group-theoretic concepts and results for Leibniz algebras
DOI:
https://doi.org/10.15407/dopovidi2018.01.010Keywords:
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 centerAbstract
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.
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