Noncommutative Line Bundles and Morita Equivalence

  • B. Jurco
ITP - Hörsaal 1 Universität Leipzig, ITP (Leipzig)


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 Morita equivalent star product.

9/25/01 9/29/01

Noncommutative Geometry, Strings and Renormalization

Universität Leipzig, ITP ITP - Hörsaal 1

H. Grosse

G. Rudolph

Klaus Sibold

Julius Wess

Eberhard Zeidler