Continuous perturbations of noncommutative Euclidean spaces and tori

Li Gao

Continuous perturbations of noncommutative Euclidean spaces and tori

Operator Algebras 2016-12-01 v2

Authors: Li Gao

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.

Keywords

noncommutative Euclidean spaces noncommutative tori continuous perturbations rotation C*-algebras Moyal deformation Lipschitz continuous maps

Cite

@article{arxiv.1605.06846,
  title  = {Continuous perturbations of noncommutative Euclidean spaces and tori},
  author = {Li Gao},
  journal= {arXiv preprint arXiv:1605.06846},
  year   = {2016}
}

Comments

v2: 28 pages, several additions and modifications throughout

Continuous perturbations of noncommutative Euclidean spaces and tori

Abstract

Keywords

Cite

Comments

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