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

Dräxler, Peter; Kögerler, Klara

doi:10.1090/S0025-5718-01-01404-1

An algorithm for finding all preprojective components of the Auslander-Reiten quiver
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by Peter Dräxler and Klara Kögerler;

Math. Comp. 71 (2002), 743-759

DOI: https://doi.org/10.1090/S0025-5718-01-01404-1

Published electronically: December 21, 2001

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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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