Seminar "Combinatorics of Vassiliev invariants". Speaker: Boris Bychkov

Many graph invariants allow an extension to Hopf algebra homomorphisms from the Hopf algebra of graphs to other Hopf algebras, like polynomial ones. Such a homomorphism is uniquely determined by its values on primitive elements in the Hopf algebra of graphs. These values are very simple, since they also are primitive elements, hence linear polynomials. Hence, understanding primitive elements plays a crucial role in understanding polynomial graph invariants. In particular, we will discuss the projection of the Hopf algebra of graphs to its primitive subspace.