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arXiv · 1512.05621

Bilinear forms on Green rings of finite dimensional Hopf algebras

Z. Wang·L. Li·Y. Zhang
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Abstract

In this paper, we study the Green ring and the stable Green ring of a Hopf algebra $H$ by means of bilinear forms. We show that the Green ring of a Hopf algebra of finite representation type is a Frobenius algebra over $\mathbb{Z}$ with a dual basis associated to almost split sequences. On the stable Green ring we define a new bilinear form which is more accurate to determine the bi-Frobenius property of the stable Green ring. We show that the complexified stable Green ring (or algebra) is a group-like algebra, and hence a bi-Frobenius algebra, if the bilinear form on the stable Green ring is non-degenerate.

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BibTeXRIS

Z. Wang, L. Li, Y. Zhang. 2016-04-01. Bilinear forms on Green rings of finite dimensional Hopf algebras. https://arxiv.org/abs/1512.05621

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