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arXiv · 2205.00947

On total stability conditions for Dynkin quivers

Rene Marczinzik
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Abstract

We show that for a Dynkin quiver $Q$ of type $E_7$ with a specific orientation, the path algebra $KQ$ has no slope function of the form $\mu=\frac{\theta}{\dim}$ that defines a total stability condition. This gives a counterexample to a conjecture of Reineke.

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Rene Marczinzik. 2022-05-02. On total stability conditions for Dynkin quivers. https://arxiv.org/abs/2205.00947

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