The isomorphism problem for cyclic blocks and their source algebras (Q1922556)

The structure of blocks with cyclic defect groups is determined in terms of their source algebras, thus confirming a conjecture of the author that the source algebras of such a block are essentially determined by an endo-permutation module of the defect group and the Brauer tree of the block. In fact, it is shown that blocks satisfy an analog of the isomorphism problem for group algebras. Thus, normalizing suitably, the group of units of the block algebra has a unique conjugacy class of subgroups isomorphic to the defect group.