Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Journal of Lie Theory 17 (2007), No. 1, 091--098Copyright Heldermann Verlag 2007 Almost Horospherical Subalgebras of Semisimple Lie Algebras Alexander V. Smirnov Scientific Research Computing Center, Moscow State University, 119992 Moscow, Russia asmirnov@rdm.ru [Abstract-pdf] \def\g{{\frak g}}\def\h{{\frak h}} 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 $\h\subset\g$ such that every subalgebra strictly containing $\h$ is horospherical, i.e., contains a maximal unipotent subalgebra of $\g$. Keywords: Lie algebras, parabolic induction. MSC: 17B45 [ Fulltext-pdf  (180  KB)] for subscribers only.