Non-Associative Geometry of Quantum Tori
Francesco D'Andrea, Davide Franco
TL;DR
This paper introduces a novel geometric framework for quantum tori using a principal bundle approach, connecting noncommutative geometry with deformations of classical manifolds.
Contribution
It presents a new method to construct imprimitivity bimodules for noncommutative tori via a principal bundle construction involving a quasi-associative deformation.
Findings
Imprimitivity bimodules derived from principal bundle construction.
Connection between noncommutative tori and deformed Heisenberg manifolds.
New geometric perspective on quantum tori.
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.
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