On stable blocks of Auslander-algebras

Riedtmann, Christine

doi:10.1090/S0002-9947-1984-0737881-3

On stable blocks of Auslander-algebras
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Trans. Amer. Math. Soc. 283 (1984), 485-505 Request permission

Abstract:

The Auslander-algebra ${E_\Lambda }$ of an algebra $\Lambda$ of finite representation type is the endomorphism algebra of the direct sum $M = \oplus {M_i}$ of one copy of each indecomposable $\Lambda$-module. A stable block of ${E_\Lambda }$ is a connected direct factor of the residue algebra of ${E_\Lambda }$ modulo the two-sided ideal generated by the projections of $M$ to the ${M_i}$’s that are not stable under $DTr$. This paper describes the stable blocks whose quiver is a stable translation-quiver of class ${A_n}$ or ${D_n}$.

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