Geodesic
Representation theory of two-dimensionalbrauer graph rings
Colloquium Mathematicum, Tome 86 (2000) no. 2, pp. 239-251

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/cm-86-2-239-251
Keywords: Brauer graph, order, Cohen-Macaulay, Auslander-Reiten quiver

Wolfgang Rump 1

1 
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Wolfgang Rump. Representation theory of two-dimensionalbrauer graph rings. Colloquium Mathematicum, Tome 86 (2000) no. 2, pp. 239-251. doi: 10.4064/cm-86-2-239-251

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