Shadow of noncommutativity
Résumé
We analyse the structure of the $\\kappa=0$ limit of a family of algebras $A_\\kappa$ describing noncommutative versions of space-time, with $\\kappa$ a parameter of noncommutativity. Assuming the Poincar\\é covariance of the $\\kappa=0$ limit, we show that, besides the algebra of functions on Minkowski space, $A_0$ must contain a nontrivial extra factor $A^I_0$ which is Lorentz covariant and which does not commute with the functions whenever it is not commutative. We give a general description of the possibilities and analyse some representative examples.