Universal R-matrix for esoteric quantum group

Abstract

The universal $R$-matrix for a class of esoteric (non-standard) quantum groups ${\mathcal{U}}_q(gl(2N+1))$ is constructed as a twisting of the universal $R$-matrix ${\mathcal{R}}_S$ of the Drinfeld-Jimbo quantum algebras. The main part of the twisting element $\mathcal{F}$ is chosen to be the canonical element of appropriate pair of separated Hopf subalgebras (quantized Borel's $\mathcal{B}(N)\subset {\mathcal{U}}_q(gl(2N+1))$), providing the factorization property of $\mathcal{F}$. As a result, the esoteric quantum group generators can be expressed in terms of the Drinfeld-Jimbo ones.

12 pages, LaTeX