Coalgebra Gauge Theory

Abstract

We develop a generalised gauge theory in which the role of gauge group is played by a coalgebra and the role of principal bundle by an algebra. The theory provides a unifying point of view which includes quantum group gauge theory, embeddable quantum homogeneous spaces and braided group gauge theory, the latter being introduced now by these means. Examples include ones in which the gauge groups are the braided line and the quantum plane.

32 pages, LaTeX, uses epsf

Cited by in corpus (23)

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• Conceptual Issues for Noncommutative Gravity on Algebras and Finite Sets
• Classifying bicrossed products of Hopf algebras
• On the 2-categories of weak distributive laws
• Integrals, quantum Galois extensions and the affineness criterion for quantum Yetter-Drinfel'd modules
• Advances in Quantum and Braided Geometry
• Hopf fibration and monopole connection over the contact quantum spheres
• Diagrammatics of Braided Group Gauge Theory
• The coisotropic subgroup structure of SL_q(2,R)
• Connections over twisted tensor products of algebras
• Crossed Product Structure of Quantum Euclidean Groups
• An algebraic framework for noncommutative bundles with homogeneous fibres
• Crossed Products by a Coalgebra
• Pre-torsors and Galois comodules over mixed distributive laws
• Induction of quantum group representations
• On the Relationship between Classical and Deformed Hopf Fibrations
• Semi-entwining structures and their applications
• Some Remarks on Quantum and Braided Group Gauge Theory
• Principal bundles in the category of ${\mathbb{Z}}_2^n$-manifolds
• Bicategory of entwinings