The source algebras of blocks with a Klein four defect group
Let \(\mathcal O\) be a complete discrete valuation ring with algebraically closed residue field of characteristic 2, and let \(G\) be a finite group. The author shows that the source algebra of a 2-block of \(G\) with Klein four defect group \(P\) is isomorphic as an interior \(P\)-algebra to an iterated Heller translate of either \({\mathcal O}P\) or \({\mathcal O}A_ 4\) or to the principal block algebra of \({\mathcal O}A_ 5\) (where the Heller translate of an interior \(P\)-algebra is defined in terms of the \(\mathcal O\)- endomorphism ring of the Heller translate of the trivial module). This result extends the work of R. Brauer and K. Erdmann on such blocks.
scientific article; zbMATH DE number 638519