Continuous perturbations of noncommutative Euclidean spaces and tori

Abstract

We prove a noncompact version of Haagerup and Rørdam's result about continuous paths of the rotation $C^{\ast }$-algebras. It gives a continuous Moyal deformation of Euclidean plane. Moveover, the construction is generalized to noncommutative Euclidean spaces of dimension $d\ge 2$. As a corollary, we obtain Lip${}^{\frac{1}{2}}$ continuous maps for the generators of noncommutative $d$-tori.

v2: 28 pages, several additions and modifications throughout

References in corpus (1)

• Algebras of distributions suitable for phase-space quantum mechanics. I

Cited by in corpus (2)

• Dilations of unitary tuples
• Bounded perturbations of the Heisenberg commutation relation via dilation theory