Space-Time Symmetries of Noncommutative Spaces

We define a noncommutative Lorentz symmetry for canonical noncommutative spaces. Although the Lie algebra of the Poincaré group is undeformed, the noncommutative vector fields and the derivatives transform under a deformed Lorentz transformation. We apply our idea to the case of actions obtained by expanding the star product and the fields taken in the enveloping of the Lie algebra via the Seiberg-Witten maps and verify that these actions are invariant under these new noncommutative Lorentz transformations. We finally consider general coordinate transformations and show that the metric is undeformed. ∗[email protected]