Galois coverings of weakly shod algebras

TL;DR

This paper explores the Galois coverings of weakly shod algebras, establishing a correspondence with their connecting components and linking simple connectivity to Hochschild cohomology.

Contribution

It provides a new correspondence between Galois coverings of weakly shod algebras and their components, and characterizes simple connectivity via Hochschild cohomology.

Findings

Galois coverings correspond to those of connecting components

Weakly shod algebra is simply connected iff its Hochschild cohomology vanishes

Provides criteria for simple connectivity in terms of cohomology

Abstract

We investigate the Galois coverings of weakly shod algebras. For a weakly shod algebra not quasi-tilted of canonical type, we establish a correspondence between its Galois coverings and the Galois coverings of its connecting component. As a consequence, we show that a weakly shod algebra is simply connected if and only if its first Hochschild cohomology group vanishes.