Modular Double of Quantum Group

TL;DR

This paper introduces a new extension of quantum groups called the modular double, uniting quantum groups with dual parameters to expand their algebraic structure.

Contribution

It proposes a novel construction called the modular double, combining quantum groups with dual parameters to deepen the understanding of their algebraic properties.

Findings

Defines the modular double structure for quantum groups

Establishes duality relations between parameters q and dual q

Provides a framework for further algebraic exploration

Abstract

An extension of Quantum Group is described. We propose to unite the quantum groups with parameter q and with parameter modularly dual to q.