SPEAKER: Grace Lyo
TITLE: Semisimple skew group rings and their modules
Let E be a field equipped with the action of a finite group G. Then the skew group ring E is a mild generalization of the ordinary group ring E[G] in which the elements of E do not commute with the elements of G (instead, the group action takes place when such elements are transposed). In the case where E is semisimple and the subgroup N of elements of G that act trivially on E is abelian, I will present a means of describing the modules over E up to isomorphism as well as their endomorphism rings and tensor product structure. This is joint work with K. Ribet. In my topology talk the same day, I will use these results to verify, in a special case, a conjectural relationship between the algebraic K-theory spectrum of an arbitrary field and the semilinear representations of its absolute Galois group.