Operator Representations on Quantum Spaces

We deal with quantum spaces of particular importance in physics, i.e., q-deformed Minkowski space and q-deformed Euclidean space in three and four dimensions. For all these cases representations of their covariant differential calculi have been worked out. The explicit formulae refer to left representations, as right representations can be easily deduced from left ones. We are going to show for all cases how this can be done. Additionally, the complete Hopf structures of all considered differential calculi are listed, from which the q-deformed versions of Leibniz rules can directly be obtained. † [email protected] [email protected]