Regular extreme semisimple Lie algebras

A subalgebra of a semisimple Lie algebra is wide if every simple module of the semisimple Lie algebra remains indecomposable when restricted to the ubalgebra. A subalgebra is narrow if the restrictions of all non-trivial simple modules to the subalgebra have proper decompositions. A semisimple Lie algebra is regular extreme if any regular subalgebra of the semisimple Lie algebra is either narrow or wide. In this talk, I'll present our recent work showing that all simple Lie algebras are regular extreme; and that no non-simple, semisimple Lie algebra is regular extreme. Note that all Lie algebras and modules in this talk are finite-dimensional and over the complex numbers.