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Title

Representation theory of two-dimensionalbrauer graph rings

Authors 1

Affiliations

  1. Mathematisches Institut B/3, University of Stuttgart, Pfaffenwaldring 57, D-70550 Stuttgart, Germany

Abstract

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.

Keywords

ENG
Brauer graph, order, Cohen-Macaulay, Auslander-Reiten quiver

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Colloquium Mathematicum
2000/86/2
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Pages:
239-251
Main language of publication
English
Received
1999-03-30
Accepted
2000-02-01
Published
2000
Exact and natural sciences