Differential Calculus on Quantum Spaces and Quantum Groups

Abstract

A review of recent developments in the quantum differential calculus. The quantum group $G{L}_q(n)$ is treated by considering it as a particular quantum space. Functions on $S{L}_q(n)$ are defined as a subclass of functions on $G{L}_q(n)$. The case of $S{O}_q(n)$ 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.

23 pages

Cited by in corpus (9)

• Relativistic and Newtonian kappa spacetimes
• Poisson Algebra of Differential Forms
• Inhomogeneous quantum groups IGL_{q,r}(N): Universal enveloping algebra and differential calculus
• Induced extended calculus on the quantum plane
• Realization of Vector fields for Quantum Groups as Pseudodifferential Operators on Quantum Spaces
• All bicovariant differential calculi on Glq(3,C) and SLq(3,C)
• On construction of unitary quantum group differential calculus
• Differential Geometry of the Lie superalgebra of the quantum superplane
• On Poisson-Lie structure on the external algebra of the classical Lie groups