Geometry of Quantum Principal Bundles II-Extended Version

Abstract

A general noncommutative-geometric theory of principal bundles is presented. Quantum groups play the role of structure groups. General quantum spaces play the role of base manifolds. A differential calculus on quantum principal bundles is studied. In particular, algebras of horizontal and verticalized differential forms on the bundle are introduced and investigated. The formalism of connections is developed. Operators of horizontal projection, covariant derivative and curvature are constructed and analyzed. A quantum generalization of classical Weil's theory of characteristic classes is sketched. Quantum analogs of infinitesimal gauge transformations are studied. Illustrative examples and constructions are presented.

72 pages, (AMS-LaTeX)

References in corpus (2)

• Geometry of Quantum Principal Bundles I
• Characteristic Classes of Quantum Principal Bundles

Cited by in corpus (7)

• Quantum Principal Bundles and Corresponding Gauge Theories
• Dunkl Operators as Covariant Derivatives in a Quantum Principal Bundle
• Topics in Noncommutative Geometry
• Classical gauge theory on quantum principal bundles
• On Differential Structures on Quantum Principal Bundles
• Quantum Principal Bundles and Tannaka-Krein Duality Theory
• Dunkl Operators for Arbitrary Finite Groups