Non-Commutative Geometry and Twisted Conformal Symmetry

Abstract

The twist-deformed conformal algebra is constructed as a Hopf algebra with twisted co-product. This allows for the definition of conformal symmetry in a non-commutative background geometry. The twisted co-product is reviewed for the Poincar\'e algebra and the construction is then extended to the full conformal algebra. It is demonstrated that conformal invariance need not be viewed as incompatible with non-commutative geometry; the non-commutativity of the coordinates appears as a consequence of the twisting, as has been shown in the literature in the case of the twisted Poincar\'e algebra.