$\kappa$-Minkowski as tangent space I: quantum partition of unity

Abstract

We define a quantum (noncommutative) analogue of locally trivial tangent bundle based on two main elements: the definition of local algebras through quotients of ideals of the global algebra as introduced in [21], and the triviality of the local tangent space as being the $\kappa$-Minkowski space inspired from [2]. This tangent bundle is explicitly constructed via local coordinate charts. Every local objects are exported to the global algebra through the notion of quantum (noncommutative) partition of unity introduced in this purpose. This partition is also used to export consistently an integral on $\kappa$-Minkowski to an integral on the global algebra.