Abstract
We study the flatness for the moment map associated to the cotangent bundle of the space of representations of a quiver Q. If the associated moment map of a root is flat, then we call the root a flat root. We first study the flat roots in the fundamental set of a quiver Q. Then we give an explicit description of all the flat roots of Q. This description is obtained by using the natural class of (−1)-reflections, which are introduced in this paper. We also show that there are only a finite number of flat roots in each orbit under the Weyl-group of the quiver Q.
Original language | English |
---|---|
Pages (from-to) | 105-119 |
Number of pages | 15 |
Journal | Journal of Algebra |
Volume | 298 |
Issue number | 1 |
Early online date | 28 Jan 2006 |
DOIs | |
Publication status | Published - 1 Apr 2006 |