On total stability conditions for Dynkin quivers

Published 2 May 2022 in math.RT | (2205.00947v1)

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

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