On the role played by anticommutativity in Leibniz algebras

1Kurdachenko, LA, 2Semko, NN, 3Subbotin, IYa.
1Oles Honchar Dnipropetrovsk National University
2State Tax Service National University of Ukraine, Irpin
3National University, Los Angeles, USA
Dopov. Nac. akad. nauk Ukr. 2019, 1:3-9
https://doi.org/10.15407/dopovidi2019.01.003
Section: Mathematics
Language: English
Abstract: 

Lie algebras are exactly the anticommutative Leibniz algebras. We conduct a brief analysis of the approach to Leibniz algebras which is based on the concept of anticenter (Lie-center) and antinilpotency (Lie nilpotentency).

Keywords: anticenter, anticentral series, center, central series, Leibniz algebra, Lie algebra, Lie-center, Lie-central series
References: 

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