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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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The Auslander-Reiten quiver of a simple curve singularity
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by Ernst Dieterich and Alfred Wiedemann PDF
Trans. Amer. Math. Soc. 294 (1986), 455-475 Request permission

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
  • © Copyright 1986 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 294 (1986), 455-475
  • MSC: Primary 14H20; Secondary 13C05, 16A64
  • DOI: https://doi.org/10.1090/S0002-9947-1986-0825715-X
  • MathSciNet review: 825715