Almost horospherical subalgebras of semisimple Lie algebras

It is well known that the maximal subalgebras of a semisimple Lie algebra g are certain semisimple subalgebras and the maximal parabolic subalgebras. This paper provides a classification of subalgebras h subset of g such that every subalgebra strictly containing h is horospherical, i.e., contains a maximal unipotent subalgebra of g.