Journal of Operator Theory
Volume 79, Issue 1, Winter 2018 pp. 173-200.
Continuous perturbations of noncommutative Euclidean spaces and tori
Authors:
Li Gao
Author institution: Department of Mathematics, University of Illinois, Urbana, IL 61801, U.S.A.
Summary: We prove the existence of the Lip$^{1/2}$ continuous Moyal deformation
of Euclidean plane. It is a noncompact version of Haagerup and Rordam's result about
continuous paths of the rotation $C^*$-algebras.
Moveover, our construction is generalized to noncommutative Euclidean spaces of d
imension $d\geqslant 2$. As a corollary, we extend Haagerup and Rordam's result
to noncommutative $d$-tori.
DOI: http://dx.doi.org/10.7900/jot.2017feb09.2156
Keywords: Moyal deformation, noncommutative Euclidean space, noncommutative tori
Contents
Full-Text PDF