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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The Auslander-Reiten quiver of a simple curve singularity


Authors: Ernst Dieterich and Alfred Wiedemann
Journal: Trans. Amer. Math. Soc. 294 (1986), 455-475
MSC: Primary 14H20; Secondary 13C05, 16A64
MathSciNet review: 825715
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Abstract: With any simple curve singularity (plane, complex, affine-algebraic) of Dynkin-type $ \Delta $ we associate the category of all finitely generated torsionfree modules over its complete local ring. For each of these module categories we calculate the Auslander-Reiten quiver. We suggest the construction of the ``twisted quiver'' of a quiver with involution and valuation of arrows which gives rise to a (purely combinatorial) one-to-one correspondence between the Auslander-Reiten quiver and the Dynkin diagram $ \Delta $.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1986-0825715-X
PII: S 0002-9947(1986)0825715-X
Article copyright: © Copyright 1986 American Mathematical Society