Kac's Theorem for equipped graphs and for maximal rank representations

TL;DR

This paper extends Kac's Theorem to equipped graphs with relations and to quiver representations with maximal rank constraints, broadening the theorem's applicability.

Contribution

It introduces two new generalizations of Kac's Theorem, one for equipped graphs with relations and another for quivers with rank restrictions.

Findings

Generalization to equipped graphs with relations

Extension to quiver representations with maximal rank

Broader applicability of Kac's Theorem

Abstract

We give two generalizations of Kac's Theorem on representations of quivers. One is to representations of equipped graphs by relations, in the sense of Gelfand and Ponomarev. The other is to representations of quivers in which certain of the linear maps are required to have maximal rank.