Simple transitive 2-representations of 2-categories associated to self-injective cores

TL;DR

This paper classifies simple transitive 2-representations of specific 2-subcategories derived from self-injective cores of finite-dimensional algebras, expanding previous classification results significantly.

Contribution

It introduces a broad classification of simple transitive 2-representations for 2-categories linked to self-injective cores, generalizing earlier work.

Findings

Complete classification of simple transitive 2-representations

Generalization of previous classification results

New insights into 2-categories associated to self-injective cores

Abstract

Given a finite dimensional algebra $A$, we consider certain sets of idempotents of $A$, called self-injective cores, to which we associate 2-subcategories of the 2-category of projective bimodules over $A$. We classify the simple transitive 2-representations of such 2-subcategories, vastly generalizing the main result of arXiv:1805.05724.