Laplacians and gauged Laplacians on a quantum Hopf bundle

Details Laplacians and gauged Laplacians on a quantum Hopf bundle Laplacians and gauged Laplacians on a quantum Hopf bundle

2010-03-29

arxiv.org/abs/1003.5598v1

Mathematics

Quantum Algebra

59 pages; to appear on "Quantum groups and noncommutative spaces", M.Marcolli and D.Parashar (eds.)

Scientific paper

This paper presents an analysis of the set of connections and covariant derivatives on a U(1) quantum Hopf bundle on the standard Podles sphere, whose total space quantum SU(2) is equipped with the 3d left covariant differential calculus by Woronowicz. The introduction of a Hodge duality on the exterior algebras on both total and base space of the bundle allows for the study of Laplacians and of gauged Laplacians.

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