On some low dimensional quantum groups

TL;DR

This paper explores low-dimensional noncompact quantum groups as deformations of Lie groups, providing examples and methods for their construction within the context of noncommutative geometry.

Contribution

It offers a systematic presentation of examples and procedures for constructing low-dimensional quantum groups, enhancing understanding in noncommutative geometry.

Findings

Examples of noncompact quantum groups as deformations of Lie groups

General procedures for constructing low-dimensional quantum groups

Expository overview of noncommutative geometric approaches

Abstract

This paper is an adaptation of a chapter from an upcoming monograph on noncommutative geometry and quantum groups. We present examples of non compact quantum groups which are deformations of low dimensional Lie groups. The paper is of expository nature and provides both particular examples and some general procedures for constructing them.