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Quantization and Morita equivalence for constant Dirac structures on tori

Xiang Tang·Alan Weinstein
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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.

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Xiang Tang, Alan Weinstein. 2003-05-29. Quantization and Morita equivalence for constant Dirac structures on tori. https://arxiv.org/abs/math/0305413

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