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Bulletin of the London Mathematical Society Advance Access originally published online on May 6, 2008
Bulletin of the London Mathematical Society 2008 40(3):479-492; doi:10.1112/blms/bdn031
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© 2008 London Mathematical Society

Quiver representations of maximal rank type and an application to representations of a quiver with three vertices

Marcel Wiedemann

Department of Pure Mathematics
University of Leeds
Leeds
LS2 9JT
United Kingdom

Received 22 May 2007. Revision received 15 January 2008.

We introduce the notion of ‘maximal rank type’ for representations of quivers, which requires certain collections of maps involved in the representation to be of maximal rank. We show that real root representations of quivers are of maximal rank type. By using the maximal rank type property and universal extension functors we construct all real root representations of a particular wild quiver with three vertices. From this construction it follows that real root representations of this quiver are tree modules. Moreover, formulae given by Ringel can be applied to compute the dimension of the endomorphism ring of a given real root representation.

2000 Mathematics Subject Classification 16G20.


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