NTAG Seminar: Derivations on finite group algebras

If an algebra is semi-simple then all of its derivations are inner, although the converse need not hold. Matchke's theorem says that a finite group algebra kG is not semi-simple if and only if the characteristic of the field k divides the order of the group G. It is a fact that kG always possesses a non-inner derivation in this case, although, somewhat concerningly, we only know this by checking with the classification of finite simple groups. Linckelmann has made a stronger conjecture that an analogous statement holds for the blocks of kG. I'll talk about all this and how one can attack the problem using tricks with Hochschild cohomology. This is all joint work with Lleonard Rubio y Degrassi.