The characteristic classes of Morita equivalent star products on symplectic manifolds

Abstract

In this paper we give a complete characterization of Morita equivalent star products on symplectic manifolds in terms of their characteristic classes: two star products $\star$ and ${\star }^{\prime }$ on $(M,\omega )$ are Morita equivalent if and only if there exists a symplectomorphism $\psi :M⟶M$ such that the relative class $t(\star ,{\psi }^{\ast }({\star }^{\prime }))$ is $2 π\im$-integral. For star products on cotangent bundles, we show that this integrality condition is related to Dirac's quantization condition for magnetic charges.

22 pages. A few corrections made to Sections 3.2 and 3.3

References in corpus (5)

• Noncommutative gauge theory for Poisson manifolds
• Variations on deformation quantization
• Noncommutative line bundle and Morita equivalence
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• Deformation Quantization of Hermitian Vector Bundles

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