# Representation theory of two-dimensionalbrauer graph rings

Colloquium Mathematicae (2000)

- Volume: 86, Issue: 2, page 239-251
- ISSN: 0010-1354

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topRump, Wolfgang. "Representation theory of two-dimensionalbrauer graph rings." Colloquium Mathematicae 86.2 (2000): 239-251. <http://eudml.org/doc/210853>.

@article{Rump2000,

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.},

author = {Rump, Wolfgang},

journal = {Colloquium Mathematicae},

keywords = {Brauer graph; order; Cohen-Macaulay; Auslander-Reiten quiver; orders; Cohen-Macaulay modules; Hecke algebras; lattices; Brauer graph orders},

language = {eng},

number = {2},

pages = {239-251},

title = {Representation theory of two-dimensionalbrauer graph rings},

url = {http://eudml.org/doc/210853},

volume = {86},

year = {2000},

}

TY - JOUR

AU - Rump, Wolfgang

TI - Representation theory of two-dimensionalbrauer graph rings

JO - Colloquium Mathematicae

PY - 2000

VL - 86

IS - 2

SP - 239

EP - 251

AB - 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.

LA - eng

KW - Brauer graph; order; Cohen-Macaulay; Auslander-Reiten quiver; orders; Cohen-Macaulay modules; Hecke algebras; lattices; Brauer graph orders

UR - http://eudml.org/doc/210853

ER -

## References

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