Simple Lie Algebras, K3 Surfaces and Rozansky-Witten Invariants

 Kapranov's approach to Rozhansky-Witten invariants requires
interpreting Atiyah class of a holomorphic symplectic manifold as a product in
a "Lie algebra". We will discuss whether this "Lie algebra" is "simple",
i.e., whether it admits a specialization from Vogel's universal simple
Lie algebra. In the case of K# surfaces, the answer depends on the symmetric plurigenera
of the surface.