Finite dimensional algebras with vanishing Hochschild cohomology
Let \(Q\) be a finite quiver and \(A=kQ/I\) the basic algebra for an admissible ideal \(I\) and algebraically closed field \(k\). The authors analyze connections between vanishing of the higher Hochschild cohomologies \(H^i(A)\) and some properties of the quiver \(Q\). For instance, \(Q\) has no oriented cycles provided that the cohomology group \(H^1(A)\) strongly vanishes. Some features of the Auslander-Reiten quiver of an algebra are studied as well.
scientific article; zbMATH DE number 1271641
scientific article