Affine Lie algebras are universal central extensions of algebras of matrices over Laurent polynomials. In the case of sl_2, the ring of Laurent polynomials can be replaced with any unital Jordan algebra. This gives a very large family of Lie algebras. Motivated by this connection between Lie and Jordan theory, we describe a category of Lie algebra weight modules, whose homological properties are related to the long-standing open problem of computing graded dimensions of free Jordan algebras. No prior knowledge of Jordan algebras will be assumed. This talk is based on joint work with Olivier Mathieu.
K3 Surfaces (cont.)