Special biserial algebras with no outer derivations

Abstract

Let $A$ be a special biserial algebra over an algebraically closed field. We show that the first Hohchshild cohomology group of $A$ with coefficients in the bimodule $A$ vanishes if and only if $A$ is representation finite and simply connected (in the sense of Bongartz and Gabriel), if and only if the Euler characteristic of $Q$ equals the number of indecomposable non uniserial projective injective $A$-modules (up to isomorphism). Moreover, if this is the case, then all the higher Hochschild cohomology groups of $A$ vanish.

13 pages, submitted

References in corpus (2)

• Topological invariants of piecewise hereditary algebras
• Coverings of Laura Algebras: the Standard Case

Cited by in corpus (1)

• Representation-finite tensor product of simply connected algebras