On the Hopf algebras generated by the Yang-Baxter R-matrices

TL;DR

This paper revisits a method for constructing quasitriangular Hopf algebras from Yang-Baxter R-matrices, clarifies the underlying algebraic structures, and provides a new example with its universal R-matrix expressed as a formal power series.

Contribution

It reformulates and clarifies a recent method for building Hopf algebras from R-matrices, introducing a new example with explicit universal R-matrix.

Findings

Provided a new example of a quasitriangular Hopf algebra

Elucidated the algebraic structures underlying the method

Presented the universal R-matrix as a formal power series

Abstract

We reformulate the method recently proposed for constructing quasitriangular Hopf algebras of the quantum-double type from the R-matrices obeying the Yang-Baxter equations. Underlying algebraic structures of the method are elucidated and an illustration of its facilities is given. The latter produces an example of a new quasitriangular Hopf algebra. The corresponding universal R-matrix is presented as a formal power series.