Semi-invariants of quivers as determinants

M. Domokos, A. N. Zubkov

Research output: Contribution to journalArticlepeer-review

56 Citations (Scopus)

Abstract

A representation of a quiver is given by a collection of matrices. Semi-invariants of quivers can be constructed by taking admissible partial polarizations of the determinant of matrices containing sums of matrix components of the representation and the identity matrix as blocks. We prove that these determinantal semi-invariants span the space of all semi-invariants for any quiver and any infinite base field. In the course of the proof we show that one can reduce the study of generating semi-invariants to the case when the quiver has no oriented paths of length greater than one.

Original languageEnglish
Pages (from-to)9-24
Number of pages16
JournalTransformation Groups
Volume6
Issue number1
DOIs
Publication statusPublished - Mar 2001
Externally publishedYes

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology

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