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Let $Q$ be a quiver. Then we can use mutation (in the cluster algebra setting) to obtain a new quiver $Q'$ and to each such a quiver $Q'$ there corresponds a unique cluster-tilted algebra, which is a finite dimensional 1-Iwanaga-Gorenstein quiver algebra $K Q'/I$. The quiver $Q'$ of this algebra already determine the relations $I$.

Question: Having only the quiver $Q'$, what is the easiest way to determine the (if possible minimal) relations $I$?

I saw an indirect way using tilted algebras of type $Q$, but I wonder what is the best way to see the relations directly from the quiver $Q'$. Maybe there is a good survey on such results as I am not too familiar with the theory of cluster (tilted) algebras.

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  • $\begingroup$ Using mutation of quivers with potentials ? $\endgroup$
    – F. C.
    Commented Apr 20 at 6:18

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