Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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



Auslander-Reiten triangles in derived categories of finite-dimensional algebras

Author: Dieter Happel
Journal: Proc. Amer. Math. Soc. 112 (1991), 641-648
MSC: Primary 16G70; Secondary 16D90
MathSciNet review: 1045137
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 16G70, 16D90

Retrieve articles in all journals with MSC: 16G70, 16D90

Additional Information

Keywords: Repetitive algebras, Auslander-Reiten triangles
Article copyright: © Copyright 1991 American Mathematical Society