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Alessandro Zucca

Publications and source records attributed to Alessandro Zucca.

2 recordsLinked to original sources
arXiv2013

Dirac operator on noncommutative principal circle bundles

We study spectral triples over noncommutative principal U(1)-bundles of arbitrary dimension and formulate a compatibility condition between the connection and the Dirac operator on the total space and on the base space of the bundle. Examples of low dimensional noncommutative tori are analyzed in more detail and all connections found that are compatible with an admissible Dirac operator. Conversely, a family of new Dirac operators on the noncommutative tori, which arise from the base-space Dirac operator and a suitable connection is exhibited. These examples are extended to the theta-deformed principal U(1)-bundle S^3_θ-> S^2.

math.QA↗
arXiv2013

Dirac operators on noncommutative principal torus bundles

Spectral triples over noncommutative principal $\T^n$-bundles are studied, extending recent results about the noncommutative geometry of principal U(1)-bundles. We relate the noncommutative geometry of the total space of the bundle with the geometry of the base space. Moreover, strong connections are used to build new Dirac operators. We discuss as a particular case the commutative case, the noncommutative tori and theta deformed manifolds.

math.QA↗