Abstract
A finite-dimensional Lie algebra L over a field F is called elementary if each of its subalgebras has trivial Frattini ideal; it is an A-algebra if every nilpotent subalgebra is abelian. The present paper is primarily concerned with the classification of elementary Lie algebras. In particular, we provide a complete list in the case when F is algebraically closed and of characteristic different from 2, 3, reduce the classification over fields of characteristic 0 to the description of elementary semisimple Lie algebras, and identify the latter in the case when F is the real field. Additionally it is shown that over fields of characteristic 0 every elementary Lie algebra is almost algebraic; in fact, if L has no non-zero semisimple ideals, then it is elementary if and only if it is an almost algebraic A-algebra.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
