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2000 | 86 | 2 | 239-251
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Representation theory of two-dimensionalbrauer graph rings

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We consider a class of two-dimensional non-commutative Cohen-Macaulay rings to which a Brauer graph, that is, a finite graph endowed with a cyclic ordering of edges at any vertex, can be associated in a natural way. Some orders Λ over a two-dimensional regular local ring are of this type. They arise, e.g., as certain blocks of Hecke algebras over the completion of $ℤ[q,q^{-1}]$ at (p,q-1) for some rational prime $p$. For such orders Λ, a class of indecomposable maximal Cohen-Macaulay modules (see introduction) has been determined by K. W. Roggenkamp. We prove that this list of indecomposables of Λ is complete.
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  • Mathematisches Institut B/3, University of Stuttgart, Pfaffenwaldring 57, D-70550 Stuttgart, Germany
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