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arXiv · 1401.1885

The Green rings of minimal Hopf quivers

Hua-Lin Huang·Yuping Yang
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Abstract

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.

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Hua-Lin Huang, Yuping Yang. 2014-01-09. The Green rings of minimal Hopf quivers. https://arxiv.org/abs/1401.1885

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