Abstract

If G is a finite group and D is a finite dimensional G-graded division algebra over k, then restricting scalars to F, the algebraic closure of k, we obtain a finite dimensional G-graded simple algebra. In this lecture we address the problem in the opposite direction, namely if A is finite dimensional G-graded simple algebra over F (with char(F) = 0), then under which conditions it admits a G-graded division algebra form? (in the sense of descent theory). The main tools come from G-graded PI theory. These allow us to construct the corresponding generic objects. Joint work with Karasik.