The simple connectedness of tame algebras with separating almost cyclic coherent Auslander-Reiten components (Q2149534)

This is a nice paper on the simple connectedness of the class of finite-dimensional algebras over an algebraically closed field for which the Auslander-Reiten quiver admits a separating family of almost cyclic coherent components. The author shows that a tame algebra in this class is simply-connected if and only if its first Hochschild cohomology space vanishes (Theorem 1.1, page 925): if \(A\) is a tame algebra with a separating family of almost cyclic coherent components in the Auslander-Reiten quiver \(\Gamma_A\) of \(A\), then \(A\) is simply-connected if and only if \(H^1(A)=0\).