On the anticommutativity in Leibniz algebras

• Date: 2018
• Main Authors: Kurdachenko, Leonid Andreevich, Semko, Nikolaii Nikolaevich, Subbotin, Igor Yakov
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: Leibniz algebra; Lie algebra; center; Lie-center; anti- center; central series; anticentral series; Lie-central series; 17A32; 17A60; 17A99
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1251
• Journal Title: Algebra and Discrete Mathematics

Lie algebras are exactly the anticommutative Leibniz algebras. In this article, we conduct a brief analysis of the approach to Leibniz algebras which based on the concept of the anti-center (Lie-center) and antinilpotency (Lie nilpotentency).