On the anticommutativity in Leibniz algebras

• Published in: Algebra and Discrete Mathematics
• Date: 2018
• Main Authors: Kurdachenko, L.A., Semko, N.N., Subbotin, I.Ya.
• Format: Article
• Language: English
• Published: Інститут прикладної математики і механіки НАН України 2018
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/188377
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: On the anticommutativity in Leibniz algebras / L.A. Kurdachenko, N.N. Semko, I.Ya. Subbotin // Algebra and Discrete Mathematics. — 2018. — Vol. 26, № 1. — С. 97–109. — Бібліогр.: 8 назв. — англ.

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).