Continuous perturbations of noncommutative Euclidean spaces and tori

Li Gao

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arXiv · 1605.06846

Continuous perturbations of noncommutative Euclidean spaces and tori

Li Gao

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Abstract

We prove a noncompact version of Haagerup and R{\o}rdam's result about continuous paths of the rotation $C^*$-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$^{\frac12}$ continuous maps for the generators of noncommutative $d$-tori.

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Li Gao. 2016-05-22. Continuous perturbations of noncommutative Euclidean spaces and tori. https://arxiv.org/abs/1605.06846

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