Bicrossproduct vs. twist quantum symmetries in noncommutative geometries: the case of $\varrho$-Minkowski

Abstract

We discuss the quantum Poincar\'e symmetries of the $\varrho$-Minkowski spacetime, a space characterised by an angular form of noncommutativity. We show that it is possible to give them both a bicrossproduct and a Drinfel'd twist structure. We also obtain a new noncommutative $\star$-product, which is cyclic with respect to the standard integral measure.