Almost split sequences for rational double points

Auslander, Maurice; Reiten, Idun

doi:10.1090/S0002-9947-1987-0887498-8

Almost split sequences for rational double points
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by Maurice Auslander and Idun Reiten PDF

Trans. Amer. Math. Soc. 302 (1987), 87-97 Request permission

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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