Quiver connections and bimodules of basic algebras

TL;DR

This paper introduces a bicategory framework linking bounded quivers and basic algebras, providing a new approach to classify quantum symmetries of non-semisimple finite-dimensional algebras.

Contribution

It defines quiver connections and establishes an equivalence between bicategories of quivers and basic algebras, advancing the understanding of their structural relationships.

Findings

Bicategory of bounded quivers and connections constructed

Equivalence established with bicategory of basic algebras and bimodules

Framework aids in classifying quantum symmetries of associative algebras

Abstract

Motivated by the problem of classifying quantum symmetries of non-semisimple, finite-dimensional associative algebras, we define a notion of connection between bounded quivers and build a bicategory of bounded quivers and quiver connections. We prove this bicategory is equivalent to a bicategory of basic algebras, bimodules, and intertwiners with some additional structure.