Universal Baxterization for $\mathbb{Z}$-graded Hopf algebras

TL;DR

This paper introduces a universal method for Baxterizing solutions to the Yang-Baxter equation linked with $Z$-graded Hopf algebras, exemplified through Taft algebras and $U_q[sl(2)]$, advancing algebraic solution techniques.

Contribution

It develops a universal Baxterization approach applicable to $Z$-graded Hopf algebras, with explicit examples for Taft algebras and quantum groups.

Findings

Baxterization method successfully applied to specific Hopf algebras

Explicit solutions for Taft algebras provided

Solutions for $U_q[sl(2)]$ demonstrated

Abstract

We present a method for Baxterizing solutions of the constant Yang-Baxter equation associated with $\mathbb{Z}$-graded Hopf algebras. To demonstrate the approach, we provide examples for the Taft algebras and the quantum group $U_q[sl(2)]$.