Representation theory of two-dimensionalbrauer graph rings

Rump, Wolfgang

Colloquium Mathematicae, Tome 84/85 (2000), p. 239-251 / Harvested from The Polish Digital Mathematics Library

Résumé

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.

Détail

Publié le : 2000-01-01

Zbl 0990.16013

EUDML-ID : urn:eudml:doc:210853

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