On Thévenaz' parametrization of interior \(G\)-algebras
We give a complete proof of the parametrization of primitive interior \(G\)-algebras by the \(G\)-conjugacy classes of triples \((P,B,V)\) formed by a defect group \(P\), a \(P\)-source algebra \(B\) and a \((P,B)\)-multiplicity module \(V\), more or less suggested in Lemma 9.9 and Remarks 9.10 and 9.11 in an earlier paper [J. Algebra 116, No. 1, 7-129 (1988; Zbl 0658.20004)]. Moreover, for any primitive interior \(G\)-algebra being associated with a block of \(G\), we show how to replace the multiplicity module \(V\) -- which involves \(C_ G(P)\) and, consequently, is not an invariant of the block -- by suitable block invariants.
scientific article; zbMATH DE number 567405