On sign coherence of $c$-vectors

TL;DR

This paper proves the sign-coherence of $c$-vectors for finite-dimensional algebras and characterizes modules with $c$-vector dimension vectors as bricks satisfying a finiteness condition.

Contribution

It provides a new proof of sign-coherence and characterizes modules with $c$-vector dimension vectors in terms of bricks and functorial finiteness.

Findings

Proof of sign-coherence of $c$-vectors

Characterization of modules with $c$-vector dimension vectors as bricks

Modules satisfying a functorially finiteness condition

Abstract

Given a finite dimensional algebra $A$ over an algebraically closed field, we consider the $c$-vectors such as defined by Fu in \cite{Fu2017} and we give a new proof of its sign-coherence. Moreover, we characterise the modules whose dimension vectors are $c$-vectors as bricks respecting a functorially finiteness condition.