Jos in 't panhuis (Eindhoven): A new construction of the simply laced simple Lie algebras from affine Dynkin diagrams

We will consider Lie algebras L generated by extremal elements modulo the commutation relations given by a finite simple graph G. The generating elements correspond to the vertices of G and two of these generating elements commute if they are non-adjacent. We will show that if G is a simply laced Dynkin diagram of affine type then the corresponding Lie algebra L is "almost always" isomorphic to the simple finite-dimensional Lie algebra g whose Dynkin diagram is the corresponding finite diagram. To be more specific, from the diagram G we construct a parameter space in which "generic" points correspond to g.