Automorphisms of blocks of group algebras and character values (Q1359067)

Let \(G\) be a finite group, \(\chi\) an irreducible complex character of \(G\) and \(A(\chi)\) the block ideal of the group algebra \(\mathbb{Q} G\) related to \(\chi\). The aim of this paper is to study the group \(\Aut(A(\chi))\) of all ring (or \(\mathbb{Q}\)-algebra) automorphisms of \(A(\chi)\). Especially we are interested in the existence of subgroups \(\widetilde\Gamma\) of \(\Aut(A(\chi))\), which are isomorphic to a given subgroup \(\Gamma\) of the Galois group of the field of character values \(\mathbb{Q}(\chi)\) over the rationals. In this context we prove some results related to character values.