  In by now classical work, K. Erdmann classified blocks of finite groups with
dihedral defect groups (and more generally algebras of dihedral type) up to
Morita equivalence. In the explicit description by quivers and relations of
such algebras with two simple modules, several subtle problems about scalars
occurring in relations remained unresolved. In particular, for the dihedral
case it is a longstanding open question whether blocks of finite groups can
occur for both possible scalars 0 and 1. In this article, using Kuelshammer
ideals (a.k.a. generalized Reynolds ideals), we provide the first examples of
blocks where the scalar is 1, thus answering the above question to the
affirmative. Our examples are the principal blocks of PGL_2(F_q), the
projective general linear group of 2x2-matrices with entries in the finite
field F_q, where q=p^n\equiv \pm 1 mod 8, with p an odd prime number.
