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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

An algorithm for finding all preprojective components of the Auslander-Reiten quiver


Authors: Peter Dräxler and Klara Kögerler
Journal: Math. Comp. 71 (2002), 743-759
MSC (2000): Primary 16G20, 16G70; Secondary 05C38, 05E99
Published electronically: December 21, 2001
MathSciNet review: 1885625
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Abstract: The Auslander-Reiten quiver of a finite-dimensional associative algebra $A$encodes information about the indecomposable finite-dimensional representations of $A$and their homomorphisms. A component of the Auslander-Reiten quiver is called preprojective if it does not admit oriented cycles and each of its modules can be shifted into a projective module using the Auslander-Reiten translation. Preprojective components play an important role in the present research on algebras of finite and tame representation type. We present an algorithm which detects all preprojective components of a given algebra.


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Additional Information

Peter Dräxler
Affiliation: Fakultät für Mathematik, Universität Bielefeld, P.O. Box 100131, D-33501 Bielefeld, Germany

Klara Kögerler
Affiliation: Fakultät für Mathematik, Universität Bielefeld, P.O. Box 100131, D-33501 Bielefeld, Germany

DOI: http://dx.doi.org/10.1090/S0025-5718-01-01404-1
PII: S 0025-5718(01)01404-1
Keywords: Representations of algebras, Auslander-Reiten quiver, preprojective components
Received by editor(s): April 6, 1999
Received by editor(s) in revised form: July 7, 2000
Published electronically: December 21, 2001
Article copyright: © Copyright 2001 American Mathematical Society