English

Subrepresentations of Kronecker representations

Representation Theory 2007-05-23 v2

Abstract

Translated into the language of representations of quivers, a challenge in matrix pencil theory is to find sufficient and necessary conditions for a Kronecker representation to be a subfactor of another Kronecker representation in terms of their Kronecker invariants. The problem is reduced to a numerical criterion for a Kronecker representation to be a subrepresentation of another Kronecker representation in terms of their Kronecker invariants. The key to the problem is the calculation of ranks of matrices over polynomial rings. For this, a generalization and specialization approach is introduced. This approach is applied to provide a numerical criterion for a preprojective (resp. regular, preinjective) Kronecker representation to be a subrepresentation of another preprojective (resp. regular, preinjective) Kronecker representation in terms of their Kronecker invariants.

Keywords

Cite

@article{arxiv.math/0403088,
  title  = {Subrepresentations of Kronecker representations},
  author = {Yang Han},
  journal= {arXiv preprint arXiv:math/0403088},
  year   = {2007}
}

Comments

Accepted by Linear algebra and its applications