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Transactions of the American Mathematical Society

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



On stable blocks of Auslander-algebras

Author: Christine Riedtmann
Journal: Trans. Amer. Math. Soc. 283 (1984), 485-505
MSC: Primary 16A64; Secondary 16A46
MathSciNet review: 737881
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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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Keywords: Auslander-algebra, Auslander-Reiten quiver
Article copyright: © Copyright 1984 American Mathematical Society

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