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The Green Rings of Minimal Hopf Quivers

Part of: Categories with structure Grothendieck groups and $K_0$ Representation theory of rings and algebras

Published online by Cambridge University Press:  11 June 2015

Hua-Lin Huang  and
Yuping Yang
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)
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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.

Keywords

Green ringtensor categoryquiver representation

MSC classification

Secondary: 19A22: Frobenius induction, Burnside and representation rings 18D10: Monoidal categories (= multiplicative categories), symmetric monoidal categories, braided categories 16G20: Representations of quivers and partially ordered sets
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 59 , Issue 1 , February 2016 , pp. 107 - 141
Copyright
Copyright © Edinburgh Mathematical Society 2016 

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