The main result discussed in this lecture is an elementary proof of the
following theorem: If L is a simple Lie algebra over F of characteristic distinct from 2 and 3 having an extremal element that is not a sandwich, then either F has characteristic 5 and L is isomorphic to the 5-dimensional Witt algebra W_1,1(5), or L is generated by extremal elements.
We will also pay attention to the following theorem: If L is a simple Lie
algebra generated by extremal elements that are not sandwiches, then it is classical, i.e., essentially a Lie algebra of Chevalley type. This result, of which various geometric proofs are emerging (mainly thanks to Cuypers, Fleischmann, Roberts, and Shpectorov), gives a new proof of the classi cation of classical simple Lie algebras of characteristic distinct from 2 and 3. This is joint work with G abor Ivanyos and Dan Roozemond.
For the full paper, see [7]
