Hopf 2-cocycles of type $A_2$

TL;DR

This paper classifies Hopf 2-cocycles for pointed Hopf algebras of type A_2, linking them to Hochschild cohomology and providing explicit formulas under certain conditions.

Contribution

It offers a detailed computation of Hopf 2-cocycles for A_2 type algebras and characterizes those derived from Hochschild cohomology, advancing the classification theory.

Findings

Identified Hopf 2-cocycles for A_2 type algebras.

Connected cocycles to Hochschild cohomology via exponentiation.

Provided general formulas under specific hypotheses.

Abstract

We compute the Hopf 2-cocycles involved in the classification of pointed Hopf algebras of diagonal type $A_2$. When the quantum Serre relations are deformed, we characterize those cocycles that can be recovered from Hochschild cohomology, via exponentiation. We identify some hypotheses that allow us to present general formulas that apply in our setting.