On the quantum 'ax+b'group

TL;DR

This paper provides a detailed algebraic and structural analysis of the quantum 'ax+b' group, including generators, comultiplication formulas, and its interpretation as a quantization of a classical Poisson-Lie group.

Contribution

It offers a comprehensive presentation of the quantum 'ax+b' group, including explicit generators, comultiplication actions, and its connection to classical Poisson-Lie structures.

Findings

Explicit generators and formulas for comultiplication

Demonstration of the quantum 'ax+b' group as a Poisson-Lie quantization

Enhanced understanding of the algebraic structure of the quantum group

Abstract

The more detailed description of the quantum 'ax+b' group of Baaj and Skandalis is presented. In particular we give generators and present formulae for action of the comultiplication on them; it is also shown that this group is a quantization of a Poisson-Lie structure on a classical 'ax+b' group.