Noncommutative line bundle and Morita equivalence

Details Noncommutative line bundle and Morita equivalence Noncommutative line bundle and Morita equivalence

2001-06-13

arxiv.org/abs/hep-th/0106110v2

Lett.Math.Phys. 61 (2002) 171-186

Physics

High Energy Physics

High Energy Physics - Theory

17 pages

Scientific paper

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 $\star'$ which is shown to be Morita equivalent to $\star$.

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