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

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