Non-Associative Geometry of Quantum Tori

Francesco D'Andrea^ab, Davide Franco<sup>b

a</sup> Dipartimento di Matematica e Applicazioni, Università di Napoli “Federico II”, Complesso MSA, Via Cintia, 80126 Napoli, Italy
^b I.N.F.N. Sezione di Napoli, Complesso MSA, Via Cintia, 80126 Napoli, Italy

Abstract: We describe how to obtain the imprimitivity bimodules of the noncommutative torus from a “principal bundle” construction, where the total space is a quasi-associative deformation of a $3$-dimensional Heisenberg manifold.

Keywords: noncommutative torus; quasi-Hopf algebras; cochain quantization.

MSC: 58B34; 46L87; 53D55

Received: October 2, 2015; in final form February 4, 2016; Published online February 7, 2016

Language: English

DOI: 10.3842/SIGMA.2016.015

Bibliographic databases:

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ArXiv: 1509.05347