Strong Exceptional Sequences Provided by Quivers

Authors: Altmann K.¹; Hille L.²

Source: Algebras and Representation Theory, Volume 2, Number 1, March 1999 , pp. 1-17(17)

Publisher: Springer

Buy & download fulltext article:

Price: $47.00 plus tax (Refund Policy)

Abstract:

Let Q be a finite quiver without oriented cycles. Denote by U rarr M(Q) the fine moduli space of stable thin sincere representations of Q with respect to the canonical stability notion. We prove ExtlM(Q)(U, U) = 0 for all l > 0 and compute the endomorphism algebra of the universal bundle U. Moreover, we obtain a necessary and sufficient condition for when this algebra is isomorphic to the path algebra of the quiver Q. If so, then the bounded derived categories of finitely generated right k Q-modules and that of coherent sheaves on M(Q) are related via the full and faithful functor - otimes Lk Q U.

Keywords: flow polytopes; quivers; representations; toric varieties

Language: English

Document Type: Regular paper

Affiliations: 1: Institut für reine Mathematik der Humboldt-Universität zu Berlin, Ziegelstr. 13A, D-10099 Berlin, Germany. e-mail: altmann@mathematik.hu-berlin.de 2: Mathematisches Seminar der Universität Hamburg, Bundesstr. 55, D-20146 Hamburg, Germany. e-mail: hille@math.uni-hamburg.de

Publication date: 1999-03-01