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Apr 23, 2020 at 16:18 vote accept Mare
Apr 23, 2020 at 15:13 comment added Jeremy Rickard @Mare For the quiver $1\to2\to3\to4\to5$ with $\text{rad}^3=0$ consider the complex $0\to P(5)\to P(3)\to P(1)\to S(1)\to0$.
Apr 23, 2020 at 13:05 comment added Mare Thanks, I leave the thread open for some suggestions how one could make this true. Maybe one can hope this is true at least for acyclic quiver algebras, since there the possible summands of the projective terms "get smaller" in higher degrees. So one probably cant take repretitions.
Apr 23, 2020 at 12:43 history answered Jeremy Rickard CC BY-SA 4.0