On Thévenaz’ parametrization of interior \(G\)-algebras. (English) Zbl 0798.20006
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.
Reviewer: L.Puig (Paris)
MSC:
| 20C20 | Modular representations and characters |
| 20C05 | Group rings of finite groups and their modules (group-theoretic aspects) |
Keywords:
multiplicity module; source algebra; primitive interior \(G\)-algebras; defect group; block invariantsCitations:
Zbl 0658.20004References:
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