Source algebras of \(p\)-central group extensions
Let \(p\) be a prime, \(k\) an algebraically closed of characteristic \(p\), and \(\mathcal O\) a complete discrete valuation ring with residue field \(k\). Previously, the author [Invent. Math. 93, No. 1, 77-116 (1988; Zbl 0646.20010)] showed the rigidity of the source algebra of a block \(b\) of a finite group \(G\) in the class of \({\mathcal O}P\)-interior algebras having a \(P\times P\) stable \(\mathcal O\)-basis, where \(P\) is a defect group for \(b\). In the present paper, a stronger uniqueness is demonstrated, in essence, even its reduction via a central \(p\)-subgroup determines the source algebra of a block. The proof uses the theory of semicovering homomorphisms, and is motivated by the author's notion of \({\mathcal O}^*\)-groups. This is a long paper in which experts in the area will find much of interest.
scientific article; zbMATH DE number 1563185