Semi-invariants of quivers for arbitrary dimension vectors

AH Schofield, M van den Bergh

Research output: Contribution to journalArticle (Academic Journal)peer-review

58 Citations (Scopus)

Abstract

The representations of dimension vector alpha of the quiver Q can be parametrised by a vector space R(Q, alpha) on which an algebraic group G1(alpha) acts so that the set of orbits is bijective with the set of isomorphism classes of representations of the quiver. We describe the semi-invariant polynomial functions on this vector space in terms of the category of representations. More precisely, we associate to a suitable may between projective representations a semi-invariant polynomial function that describes when this map is inverted on the representation and we show that these semi-invariant polynomial functions form a spanning set of all semi-invariant polynomial functions in characteristic 0. If the quiver has no oriented cycles, we may replace consideration of inverting maps between projective representations by consideration of representations that are left perpendicular to some representation of dimension vector alpha. These left perpendicular representations are just the cokernels of the maps between projective representations that we consider.
Translated title of the contributionSemi-invariants of quivers for arbitrary dimension vectors
Original languageEnglish
Pages (from-to)125 - 138
Number of pages14
JournalIndagationes Mathematicae
Volume12 (1)
DOIs
Publication statusPublished - Mar 2001

Bibliographical note

Publisher: Elsevier Science BV
Other identifier: IDS Number: 454UG

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