Leibniz Algebras and Lie Algebras

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2013
• Main Authors: Mason, G., Yamskulna, G.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2013
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/149355
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Leibniz Algebras and Lie Algebras / G. Mason, G. Yamskulna // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 7 назв. — англ.

This paper concerns the algebraic structure of finite-dimensional complex Leibniz algebras. In particular, we introduce left central and symmetric Leibniz algebras, and study the poset of Lie subalgebras using an associative bilinear pairing taking values in the Leibniz kernel.