Notes on two-parameter quantum groups, (II)

TL;DR

This paper explores the structures and representations of two-parameter quantum groups related to simple Lie algebras, establishing an equivalence of their braided tensor categories, thus advancing understanding of their algebraic properties.

Contribution

It explicitly establishes an equivalence between the braided tensor categories of two-parameter and one-parameter quantum groups.

Findings

Equivalence of braided tensor categories $ ext{O}^{r,s}$ and $ ext{O}^q$

Deepened understanding of deformed structures of quantum groups

Extended results from previous work to two-parameter cases

Abstract

This paper is the sequel to [HP1] to study the deformed structures and representations of two-parameter quantum groups $U_{r,s}(\mathfrak{g})$ associated to the finite dimensional simple Lie algebras $\mg$. An equivalence of the braided tensor categories $\O^{r,s}$ and $\O^{q}$ is explicitly established.