Noncommutative vector bundles over fuzzy CP^N and their covariant derivatives

Abstract

We generalise the construction of fuzzy CP^N in a manner that allows us to access all noncommutative equivariant complex vector bundles over this space. We give a simplified construction of polarization tensors on S^2 that generalizes to complex projective space, identify Laplacians and natural noncommutative covariant derivative operators that map between the modules that describe noncommuative sections. In the process we find a natural generalization of the Schwinger-Jordan construction to su(n) and identify composite oscillators that obey a Heisenberg algebra on an appropriate Fock space.

34 pages, v2 contains minor corrections to the published version

References in corpus (2)

• Quantum Hall Effect in Higher Dimensions, Matrix Models and Fuzzy Geometry
• Drinfeld Twist and General Relativity with Fuzzy Spaces

Cited by in corpus (10)

• Fiber Bundles and Matrix Models
• A universal Dirac operator and noncommutative spin bundles over fuzzy complex projective spaces
• Fuzzy Toric Geometries
• Spin $j$ Dirac Operators on the Fuzzy 2-Sphere
• Large N reduction on coset spaces
• Dirac operators for matrix algebras converging to coadjoint orbits
• Laplacians on Fuzzy Riemann Surfaces
• Noncommutative Spherically Symmetric Spaces
• The fuzzy BTZ
• Unusual Thermodynamics on the Fuzzy 2-Sphere