Simple transitive 2-representations of bimodules over radical square zero Nakayama algebras via localization

TL;DR

This paper classifies simple transitive 2-representations of bimodules over radical square zero Nakayama algebras, introducing a localization method that constructs all such representations with finitary apex.

Contribution

It introduces a localization framework for 2-representations and completes the classification of simple transitive 2-representations with finitary apex in this setting.

Findings

Constructed new simple transitive 2-representations via localization.

Proved all such representations are equivalent to localizations of cell 2-representations.

Established a universal property for the localization construction.

Abstract

We study the classification problem of simple transitive 2-representations of the 2-category of finite-dimensional bimodules over a radical square zero Nakayama algebra. This results in a complete classification of simple transitive 2-representations whose apex is a finitary two-sided cell. We define a notion of localization of 2-representations. We construct previously unknown simple transitive 2-representations as localizations of cell 2-representations. Using the universal property of our construction we prove that any simple transitive 2-representation with finitary apex is equivalent to a localization of a cell 2-representation.