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Standard components of a Krull-Schmidt category

Authors: Shiping Liu and Charles Paquette
Journal: Proc. Amer. Math. Soc. 143 (2015), 45-59
MSC (2010): Primary 16G70, 16G20, 16G10
Published electronically: August 28, 2014
MathSciNet review: 3272731
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Abstract: We provide criteria for an Auslander-Reiten component having sections of a Krull-Schmidt category to be standard. Specializing to the category of finitely presented representations of a strongly locally finite quiver and its bounded derived category, we obtain many new types of standard Auslander-Reiten components. An application to the module category of a finite-dimensional algebra yields some interesting new results.

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Additional Information

Shiping Liu
Affiliation: Département de Mathématiques, Université de Sherbrooke, Sherbrooke, Québec J1K 2R1, Canada

Charles Paquette
Affiliation: Department of Mathematics and Statistics, University of New Brunswick, Fredericton, New Brunswick E3B 5A3, Canada

Keywords: Krull-Schmidt categories, almost split sequences, Auslander-Reiten quiver, standard components, representations of quivers, tilted algebras.
Received by editor(s): August 24, 2012
Received by editor(s) in revised form: January 29, 2013, and March 6, 2013
Published electronically: August 28, 2014
Additional Notes: The first-named author was supported in part by the NSERC of Canada
The second-named author was supported in full by NSERC and AARMS
Dedicated: In memory of Michael C. R. Butler
Communicated by: Birge Huisgen-Zimmermann
Article copyright: © Copyright 2014 American Mathematical Society