Differential Calculus on Quantum Spaces and Quantum Groups

TL;DR

This paper reviews recent advances in quantum differential calculus on quantum groups like $GL_q(n)$, $SL_q(n)$, and $SO_q(n)$, highlighting their structure as quantum spaces and functions defined on them.

Contribution

It provides a comprehensive overview of quantum differential calculus on various quantum groups, emphasizing their interpretation as quantum spaces and the function classes involved.

Findings

Quantum group $GL_q(n)$ treated as a quantum space

Functions on $SL_q(n)$ defined as a subclass of $GL_q(n)$ functions

Brief consideration of $SO_q(n)$ case

Abstract

A review of recent developments in the quantum differential calculus. The quantum group $GL_q(n)$ is treated by considering it as a particular quantum space. Functions on $SL_q(n)$ are defined as a subclass of functions on $GL_q(n)$. The case of $SO_q(n)$ is also briefly considered. These notes cover part of a lecture given at the XIX International Conference on Group Theoretic Methods in Physics, Salamanca, Spain 1992.