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arXiv · 1309.1088

Vanishing of self-extensions over symmetric algebras

Kosmas Diveris·Marju Purin
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Abstract

We study self-extensions of modules over symmetric artin algebras. We show that non-projective modules with eventually vanishing self-extensions must lie in AR components of stable type $\mathbb{Z}A_{\infty}$. Moreover, the degree of the highest non-vanishing self-extension of these modules is determined by their quasilength. This has implications for the Auslander-Reiten Conjecture and the Extension Conjecture.

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BibTeXRIS

Kosmas Diveris, Marju Purin. 2013-09-04. Vanishing of self-extensions over symmetric algebras. https://doi.org/10.1016/j.jpaa.2013.10.012

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