Noncommutative line bundle and Morita equivalence

Abstract

Global properties of abelian noncommutative gauge theories based on $\star$-products which are deformation quantizations of arbitrary Poisson structures are studied. The consistency condition for finite noncommutative gauge transformations and its explicit solution in the abelian case are given. It is shown that the local existence of invertible covariantizing maps (which are closely related to the Seiberg-Witten map) leads naturally to the notion of a noncommutative line bundle with noncommutative transition functions. We introduce the space of sections of such a line bundle and explicitly show that it is a projective module. The local covariantizing maps define a new star product ${\star }^{\prime }$ which is shown to be Morita equivalent to $\star$.

17 pages

References in corpus (5)

• Gauge Theory on Noncommutative Spaces
• Morita equivalence and duality
• Nonabelian noncommutative gauge theory via noncommutative extra dimensions
• Noncommutative Yang-Mills from equivalence of star products
• Noncommutative gauge theory for Poisson manifolds

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• Mirror Symmetry in Emergent Gravity
• Gauge Invariance and Noncommutativity
• Noncommutative geometry and fundamental interactions: the first ten years
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• Noncommutative gerbes and deformation quantization
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