Christian Kassel

Let G be a finite group and k a field. 

Consider the purely transcendental extension K of k generated by variables t(g) indexed by the elements of the group; the group G acts on K by h.t(g) = t(hg). 

In an article published in 1917 Emmy Noether asked whether the subfield of G-invariant elements of K is also a purely transcendental extension of k. 

It is known that the answer depends on the group G and the base field k. 

In my lecture I'll show how to extend Noether's problem to all finite-dimensional Hopf algebras and present a theorem which asserts that the answer to the generalized Noether problem is positive for all finite-dimensional pointed Hopf algebras. 

This is joint work with Akira Masuoka (University of Tsukuba).