Bernhard Böhmler, The representation dimension of k[x,y]/(x^2,y^n).

Abstract:

The representation dimension of an Artin Algebra was defined by M. Auslander in 1970. The precise value is not known in gerneral, and it is very hard to compute, even for small examples. For group algebras in characteristic 2 of rank at least 3 the precise value follows from recent work of R.Rouquier, but there's a gap for group algebras of rank 2. We shall show that for any nonnegative integer n the algebras k[x,y]/(x^2,y^(n+2)) have representation dimension 3. As a consequence, we shall obtain that the mod 2 group algebras of the groups C_2 x C_(2^m) have representation dimension 3. Note that for m > 2 these group algebras have wild representation type.