Modules over cluster-tilted algebras that do not lie on local slices

TL;DR

This paper characterizes certain indecomposable modules over cluster-tilted algebras that are not on local slices and provides an upper bound for their quantity.

Contribution

It offers a complete characterization of indecomposable transjective modules outside local slices and establishes a precise upper bound for their number.

Findings

Characterization of indecomposable transjective modules not on local slices

Sharp upper bound for the number of such modules

Applicable to arbitrary cluster-tilted algebras

Abstract

We characterize the indecomposable transjective modules over an arbitrary cluster-tilted algebra that do not lie on a local slice, and we provide a sharp upper bound for the number of (isoclasses of) these modules.