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ISSN 1088-6850(e) ISSN 0002-9947(p)

Auslander-Reiten components containing modules with bounded Betti numbers

Author(s): Edward L. Green; Dan Zacharia
Journal: Trans. Amer. Math. Soc. 361 (2009), 4195-4214.
MSC (2000): Primary 16G70; Secondary 16D50, 16E05
Posted: March 19, 2009
MathSciNet review: 2500885
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Abstract: Let be a connected selfinjective Artin algebra, and an indecomposable nonprojective -module with bounded Betti numbers lying in a regular component of the Auslander-Reiten quiver of . We prove that the Auslander-Reiten sequence ending at has at most two indecomposable summands in the middle term. Furthermore we show that the component of the Auslander-Reiten quiver containing is either a stable tube or of type $\mathbb{Z}A_{\infty}$ . We use these results to study modules with eventually constant Betti numbers, and modules with eventually periodic Betti numbers.

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