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Quotient closed subcategories of quiver representations

Published online by Cambridge University Press:  15 October 2014

Steffen Oppermann
Affiliation:
Department of Mathematics, NTNU, Trondheim, Norway email steffen.oppermann@math.ntnu.no
Idun Reiten
Affiliation:
Department of Mathematics, NTNU, Trondheim, Norway email idunr@math.ntnu.no
Hugh Thomas
Affiliation:
Department of Mathematics and Statistics, UNB, PO Box 4400, Fredericton, Canada email hugh@math.unb.ca
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Abstract

Let $Q$ be a finite quiver without oriented cycles, and let $k$ be an algebraically closed field. The main result in this paper is that there is a natural bijection between the elements in the associated Weyl group $W_{Q}$ and the cofinite additive quotient closed subcategories of the category of finite dimensional right modules over $kQ$ . We prove this correspondence by linking these subcategories to certain ideals in the preprojective algebra associated to $Q$ , which are also indexed by elements of $W_{Q}$ .

Type
Research Article
Copyright
© The Author(s) 2014 

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