Lie algebras with given properties of subalgebras and elements

Details Lie algebras with given properties of subalgebras and elements Lie algebras with given properties of subalgebras and elements

2011-05-21

arxiv.org/abs/1105.4284v2

Mathematics

Rings and Algebras

4 pages; v2: stylistic corrections

Scientific paper

Results about the following classes of finite-dimensional Lie algebras over a field of characteristic zero are presented: anisotropic (i.e., Lie algebras for which each adjoint operator is semisimple), regular (i.e., Lie algebras in which each nonzero element is regular in the sense of Bourbaki), minimal nonabelian (i.e., nonabelian Lie algebras all whose proper subalgebras are abelian), and algebras of depth 2 (i.e., Lie algebras all whose proper subalgebras are abelian or minimal nonabelian).

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