Frattini theory for N-Lie algebras

• Published in: Algebra and Discrete Mathematics
• Date: 2009
• ISSN: 1726-3255
• Main Author: Michael Peretzian Williams
• Format: Article
• Language: English
• Published: Інститут прикладної математики і механіки НАН України 2009
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/154628
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Frattini theory for N-Lie algebras / Michael Peretzian Williams
 // Algebra and Discrete Mathematics. — 2009. — Vol. 8, № 2. — С. 108–115. — Бібліогр.: 7 назв. — англ.

We develop a Frattini Theory for n-Lie algebras by extending theorems of Barnes' to the n-Lie algebra setting. Specifically, we show some sufficient conditions for the Frattini subalgebra to be an ideal and find an example where the Frattini subalgebra fails to be an ideal.