Prospecies of algebras I: Basic properties
Julian K\"ulshammer

TL;DR
This paper extends the theory of hereditary algebras to prospecies, a generalization of species, introducing new algebraic constructions and categorical equivalences.
Contribution
It develops the foundational properties of prospecies of algebras, including the construction of preprojective algebras and stable equivalences.
Findings
Constructed a preprojective algebra for prospecies
Established a stable equivalence between subcategories
Generalized hereditary algebra theory to prospecies
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 Gei\ss, Leclerc, and Schr\"oer. 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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
