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

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

2008-02-20

arxiv.org/abs/0802.2803v1

Bull. London Math. Soc. 40 (2008) 479-492

Mathematics

Representation Theory

13 pages

Scientific paper

10.1112/blms/bdn031

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.

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