Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/2623
Title: Semi-invariants of quivers for arbitrary dimension vectors
Authors: Schofield, A
VAN DEN BERGH, Michel 
Issue Date: 2001
Publisher: ELSEVIER SCIENCE BV
Source: INDAGATIONES MATHEMATICAE-NEW SERIES, 12(1). p. 125-138
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.
Notes: Univ Bristol, Dept Math, Bristol BS8 1TH, Avon, England. Limburgs Univ Ctr, Dept WNI, B-3590 Diepenbeek, Belgium.
Document URI: http://hdl.handle.net/1942/2623
ISSN: 0019-3577
e-ISSN: 1872-6100
ISI #: 000169989700010
Category: A1
Type: Journal Contribution
Validations: ecoom 2002
Appears in Collections:Research publications

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