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

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 AuslanderReiten 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 AuslanderReiten 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.

• Type: Journal
• Year: 2002
• Where: MOC
• Authors: Peter Dräxler, Klara Kögerler
• Keywords: Auslander-Reiten Quiver, Finite-dimensional Associative Algebra, Indecomposable Finite-dimensional Representations, MOC 2002