English

Quantum Heisenberg Manifolds as Twisted Groupoid $C^*$-Algebras

Operator Algebras 2014-03-24 v1

Abstract

The quantum Heisenberg manifolds are noncommutive manifolds constructed by M. Rieffel as strict deformation quantizations of Heisenberg manifolds and have been studied by various authors. Rieffel constructed the quantum Heisenberg manifolds as the generalized fixed-point algebras of certain crossed product CC^*-algebras, and they also can be realized as crossed products of C(T2)C(\mathbb{T}^2) by Hilbert CC^*-bimodules in the sense of Abadie et al. In this paper, we describe how the quantum Heisenberg manifolds can also be realized as twisted groupoid CC^*-algebras.

Keywords

Cite

@article{arxiv.1403.5313,
  title  = {Quantum Heisenberg Manifolds as Twisted Groupoid $C^*$-Algebras},
  author = {Sooran Kang and Alex Kumjian and Judith Packer},
  journal= {arXiv preprint arXiv:1403.5313},
  year   = {2014}
}