André-Quillen homology and complete intersection dimensions

Abstract

We study the relation between the vanishing of André-Quillen homology and complete intersection dimensions and we extend some of the existing results in the literature. As an application of one of our results, we give a characterization of algebra retracts of finite André-Quillen dimension with respect to complete intersection dimensions and complexity. We also investigate the relation between André-Quillen homology and an unpublished question of Foxby about complete intersection dimensions.