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Transactions of the American Mathematical Society

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

 

 

Almost split sequences for rational double points


Authors: Maurice Auslander and Idun Reiten
Journal: Trans. Amer. Math. Soc. 302 (1987), 87-97
MSC: Primary 13H10; Secondary 14B05, 16A18
DOI: https://doi.org/10.1090/S0002-9947-1987-0887498-8
MathSciNet review: 887498
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Abstract: Let $ R$ be a complete local two-dimensional integrally closed noetherian nonregular Gorenstein domain with maximal ideal $ m$ over an algebraically closed field $ k$, such that $ R/m \simeq k$. Then the category of finitely generated reflexive modules is known to have almost split sequences, and our main result is that the $ AR$-quiver is an extended Dynkin quiver $ {\tilde A_n}$, $ {\tilde D_n}$, $ {\tilde E_6}$, $ {\tilde E_7}$, or $ {\tilde E_8}$.


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DOI: https://doi.org/10.1090/S0002-9947-1987-0887498-8
Article copyright: © Copyright 1987 American Mathematical Society