Let $\k$ be a field and $Q$ a minimal Hopf quiver, i.e., a cyclic quiver or the infinite linear quiver, and let $\rep^{ ln}(Q)$ denote the category of locally nilpotent finite dimensional $\k$-representations of $Q.$ The category $\rep^{ ln}(Q)$ has natural tensor structures induced from graded Hopf structures on the path coalgebra $\k Q.$ Tensor categories of the form $\rep^{ ln} (Q)$ are an interesting class of tame hereditary pointed tensor categories which are not finite. The aim of this paper is to compute the Clebsch-Gordan formulae and Green rings of such tensor categories.
Categories: math.QA