Displaying similar documents to “A note on coalgebra gauge theory”

Quantum Fibre Bundles. An Introduction

Tomasz Brzeziński (1997)

Banach Center Publications

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An approach to construction of a quantum group gauge theory based on the quantum group generalisation of fibre bundles is reviewed.

Quantum classifying spaces and universal quantum characteristic classes

Mićo Đurđević (1997)

Banach Center Publications

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A construction of the noncommutative-geometric counterparts of classical classifying spaces is presented, for general compact matrix quantum structure groups. A quantum analogue of the classical concept of the classifying map is introduced and analyzed. Interrelations with the abstract algebraic theory of quantum characteristic classes are discussed. Various non-equivalent approaches to defining universal characteristic classes are outlined.

Some remarks on quantum and braided group gauge theory

Shahn Majid (1997)

Banach Center Publications

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We clarify some aspects of quantum group gauge theory and its recent generalisations (by T. Brzeziński and the author) to braided group gauge theory and coalgebra gauge theory. We outline the diagrammatic version of the braided case. The bosonisation of any braided group provides us a trivial principal bundle in three ways.

Quantum principal bundles and their characteristic classes

Mićo Đurđević (1997)

Banach Center Publications

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A general theory of characteristic classes of quantum principal bundles is presented, incorporating basic ideas of classical Weil theory into the conceptual framework of noncommutative differential geometry. A purely cohomological interpretation of the Weil homomorphism is given, together with a geometrical interpretation via quantum invariant polynomials. A natural spectral sequence is described. Some interesting quantum phenomena appearing in the formalism are discussed.