Quantization and Morita equivalence for constant Dirac structures on tori

TL;DR

This paper introduces a C*-algebraic quantization method for constant Dirac structures on tori, demonstrating Morita equivalence among structures in the same orbit under a specific group action, extending prior results.

Contribution

It extends the standard Poisson structure quantization to Dirac structures and proves Morita equivalence within orbits of an O(n,n|Z) action, broadening the understanding of noncommutative tori.

Findings

Established a C*-algebraic quantization for Dirac structures on tori.

Proved Morita equivalence for structures in the same O(n,n|Z) orbit.

Extended Rieffel and Schwarz's theorem to Dirac structures.

Abstract

We define a C*-algebraic quantization of constant Dirac structures on tori, which extends the standard quantization of Poisson structures. We prove that Dirac structures in the same orbit of a natural action of O(n,n|Z) give rise to Morita equivalent algebras, completing and extending a theorem of Rieffel and Schwarz.