Prospecies of algebras I: Basic properties

Abstract

In this paper, we generalise part of the theory of hereditary algebras to the context of prospecies of algebras. Here, a prospecies is a generalisation of Gabriel's concept of species gluing algebras via projective bimodules along a quiver to obtain a new algebra. This provides a categorical perspective on a recent paper by Geiß, Leclerc, and Schröer. In particular, we construct a corresponding preprojective algebra, and establish a theory of a separated prospecies yielding a stable equivalence between certain functorially finite subcategories.

To appear in: Algebra and Representation theory