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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Auslander-Reiten triangles in derived categories of finite-dimensional algebras
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by Dieter Happel PDF
Proc. Amer. Math. Soc. 112 (1991), 641-648 Request permission

Abstract:

Let $A$ be a finite-dimensional algebra. The category $bmod A$ of finitely generated left $A$-modules canonically embeds into the derived category ${D^b}\left ( A \right )$ of bounded complexes over $bmod A$ and the stable category ${\underline {\bmod } ^\mathbb {Z}}T\left ( A \right )$ of $\mathbb {Z}$-graded modules over the trivial extension algebra of $A$ by the minimal injective cogenerator. This embedding can be extended to a full and faithful functor from ${D^b}\left ( A \right )$ to $\underline {\bmod }^{\mathbb {Z}}T\left ( A \right )$. Using the concept of Auslander-Reiten triangles it is shown that both categories are equivalent only if $A$ has finite global dimension.
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Additional Information
  • © Copyright 1991 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 112 (1991), 641-648
  • MSC: Primary 16G70; Secondary 16D90
  • DOI: https://doi.org/10.1090/S0002-9939-1991-1045137-6
  • MathSciNet review: 1045137