Ext algebra of Nichols algebras of type $A_2$

TL;DR

This paper determines the full Ext algebra structure of Nichols algebras of type A2 using spectral sequences and applies this to classify the complexity of related pointed Hopf algebras, showing many are wild.

Contribution

It provides the complete Ext algebra structure for Nichols algebras of type A2 and demonstrates the wildness of certain pointed Hopf algebras with specific Dynkin diagrams.

Findings

Full Ext algebra structure of type A2 Nichols algebra obtained

Most pointed Hopf algebras with certain Dynkin types are shown to be wild

Application of Hochschild-Serre spectral sequence in algebraic structure analysis

Abstract

We give the full structure of the Ext algebra of a Nichols algebra of type $A_2$ by using the Hochschild-Serre spectral sequence. As an application, we show that the pointed Hopf algebras $u(\mathcal{D}, \lmd, \mu)$ with Dynkin diagrams of type $A$, $D$, or $E$, except for $A_1$ and $A_1\times A_1$ with the order $N_{J}>2$ for at least one component $J$, are wild.