Quantum Groups on Fibre Bundles

Abstract

It is shown that the principle of locality and noncommutative geometry can be connnected by a sheaf theoretical method. In this framework quantum spaces are introduced and examples in mathematical physics are given. With the language of quantum spaces noncommutative principal and vector bundles are defined and their properties are studied. Important constructions in the classical theory of principal fibre bundles like associated bundles and differential calculi are carried over to the quantum case. At the end $q$-deformed instanton models are introduced for every integral index.

50 pages

References in corpus (1)

• Quantum group gauge theory on quantum spaces

Cited by in corpus (12)

• Strong Connections on Quantum Principal Bundles
• Translation map in quantum principal bundles
• Connections on locally trivial quantum principal fibre bundles
• Equivariant Join and Fusion of Noncommutative Algebras
• Noncommutative principal bundles through twist deformation
• Towards a noncommutative Brouwer fixed-point theorem
• Toward a q-Deformed Standard Model
• Extended noncommutative Minkowski spacetimes and hybrid gauge symmetries
• A 4-sphere with non central radius and its instanton sheaf
• Band topology of pseudo-Hermitian phases through tensor Berry connections and quantum metric
• Quantum Homogeneous Spaces and Coalgebra Bundles
• Gauge theory models on $\kappa$-Minkowski space: Results and prospects