Simple connectedness of quasitilted algebras

TL;DR

This paper proves that a basic connected finite dimensional quasitilted algebra over an algebraically closed field is simply connected if and only if its first Hochschild cohomology group vanishes, generalizing previous results for tame cases.

Contribution

It extends the equivalence between simple connectedness and vanishing Hochschild cohomology to all quasitilted algebras, not just tame ones.

Findings

A quasitilted algebra is simply connected iff HH^1(A) = 0.

Generalizes previous results from tame to all quasitilted algebras.

Provides a characterization of simple connectedness via Hochschild cohomology.

Abstract

Let A be a basic connected finite dimensional algebra over an algebraically closed field. Assuming that A is quasitilted, we prove that A is simply connected if and only if its first Hochschild cohomology group HH^1(A) vanishes. This generalises a result of I. Assem, F.U. Coelho and S. Trepode and which proves the same equivalence for tame quasitilted algebras.