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The Green Rings of Minimal Hopf Quivers

Published online by Cambridge University Press:  11 June 2015

Hua-Lin Huang
Affiliation:
School of Mathematics, Shandong University, Jinan 250100, People's Republic of China (hualin@sdu.edu.cn; yupingyang.sdu@gmail.com)
Yuping Yang
Affiliation:
School of Mathematics, Shandong University, Jinan 250100, People's Republic of China (hualin@sdu.edu.cn; yupingyang.sdu@gmail.com)
Corresponding

Abstract

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

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 2016 

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