Dual braided quantum $E(2)$ groups

TL;DR

This paper constructs the braided dual of quantum E(2) groups over the circle group using a specific R-matrix and describes its bosonization, advancing the understanding of quantum group dualities.

Contribution

It provides an explicit construction of the braided dual and bosonization of quantum E(2) groups, which was not previously detailed.

Findings

Explicit braided dual construction over the circle group

Description of the associated bosonization

Advancement in quantum group duality understanding

Abstract

An explicit construction of the braided dual of quantum $E(2)$ groups is described over the circle group $\mathbb{T}$ with respect to a specific $R$-matrix $R$. Additionally, the corresponding bosonization is also described.