Calculi, Hodge operators and Laplacians on a quantum Hopf fibration

Abstract

We describe Laplacian operators on the quantum group SUq (2) equipped with the four dimensional bicovariant differential calculus of Woronowicz as well as on the quantum homogeneous space S2q with the restricted left covariant three dimensional differential calculus. This is done by giving a family of Hodge dualities on both the exterior algebras of SUq (2) and S2q . We also study gauged Laplacian operators acting on sections of line bundles over the quantum sphere.

v3, one reference corrected, one reference added. 31 pages

References in corpus (4)

• Holomorphic structures on the quantum projective line
• Anti-selfdual Connections on the Quantum Projective Plane: Monopoles
• Gauged Laplacians on quantum Hopf bundles
• The 3D Spin Geometry of the Quantum Two-Sphere

Cited by in corpus (5)

• Quantum Bundle Description of the Quantum Projective Spaces
• The 3D Spin Geometry of the Quantum Two-Sphere
• Derivation based differential calculi for noncommutative algebras deforming a class of three dimensional spaces
• (A class of) Hodge duality operators over the quantum SU(2)
• The $q$-linked complex Minkowski space, its real forms and deformed isometry groups