On Universal $R$-Matrix for Quantized Nontwisted Rank 3 Affine Lie Algebras

TL;DR

This paper provides explicit formulas for the universal R-matrix in quantized nontwisted rank 3 affine Lie algebras, advancing the understanding of their quantum group structures.

Contribution

It presents explicit formulas for the universal R-matrix for all quantized nontwisted rank 3 affine Lie algebras, filling a gap in the literature.

Findings

Explicit formulas for U_q(A_2^{(1)})

Explicit formulas for U_q(C_2^{(1)})

Explicit formulas for U_q(G_2^{(1)}))

Abstract

Explicit formulas of the universal $R$-matrix are given for all quantized nontwisted rank 3 affine Lie algebras $U_q(A_2^{(1)})\,,~U_q(C_2^{(1)})$ and $U_q(G_2^{(1)})$.