Coverings of Laura Algebras: the Standard Case

TL;DR

This paper investigates the covering theory of standard laura algebras, establishing conditions under which these algebras have Galois coverings and linking their Hochschild cohomology to the existence of such coverings.

Contribution

It proves that standard laura algebras have Galois coverings related to their connecting components and characterizes the vanishing of Hochschild cohomology in terms of coverings.

Findings

Standard laura algebras have Galois coverings associated with their connecting components.

The first Hochschild cohomology vanishes iff the algebra has no proper Galois coverings.

The paper clarifies the relationship between algebra coverings and Hochschild cohomology for laura algebras.

Abstract

In this paper, we study the covering theory of laura algebras. We prove that if a connected laura algebra is standard (that is, it is not quasi-tilted of canonical type and its connecting components are standard), then this algebra has nice Galois coverings associated to the coverings of the connecting component. As a consequence, we show that the first Hochschild cohomology group of a standard laura algebra vanishes if and only if it has no proper Galois coverings.