SMALL SEMISIMPLE SUBALGEBRAS OF SEMISIMPLE LIE ALGEBRAS
The goal of Section 2 is to provide a proof of Theorem 2.0.1. Section 3 introduces the necessary facts about Lie algebras and representation theory, with the goal being the proof of Proposition 3.5.7 (ultimately as an application of Theorem 2.0.1), and Proposition 3.3.1. In Section 4 we prove the main theorem, using Propositions 3.3.1 and 3.5.7. In Section 5, we apply the theorem to the special case where g is the exceptional Lie algebra G2, and k is a principal sl2-subalgebra of g. We obtain a sharp estimate of b(k, g) (in this case).