A finite dimensional algebra with cohomology ring not-finitely generated (Q689667)

We consider a specific example \(\Lambda\) of a finite dimensional algebra over an algebraically closed field \(K\). This algebra is local and basic. That is, the algebra \(\Lambda\) is given by a quiver with only one vertex 1 and loops with some relations. We prove that the cohomology ring \(\text{Ext}_ \Lambda^*(S,S)\) of the only simple \(\Lambda\)-module \(S\) is not finitely generated. We were unable to find examples as easy as this in the literature.