Abstract
The free abelian group on the set of indecomposable representations of a quiver , over a field , has a ring structure where the multiplication is given by the tensor product. We show that if is a rooted tree (an oriented tree with a unique sink), then the ring is a finitely generated -module (here is the ring modulo the ideal of all nilpotent elements). We describe the ring explicitly by studying functors from the category of representations of over to the category of finite-dimensional -vector spaces
Citation
Ryan Kinser. "Rank functions on rooted tree quivers." Duke Math. J. 152 (1) 27 - 92, 15 March 2010. https://doi.org/10.1215/00127094-2010-006
Information