Characteristic Classes of Quantum Principal Bundles

Details Characteristic Classes of Quantum Principal Bundles Characteristic Classes of Quantum Principal Bundles

1995-07-20

arxiv.org/abs/q-alg/9507017v1

Mathematics

Quantum Algebra

48 pages, AMS-LaTeX

Scientific paper

A noncommutative-geometric generalization of classical Weil theory of characteristic classes is presented, in the conceptual framework of quantum principal bundles. A particular care is given to the case when the bundle does not admit regular connections. A cohomological description of the domain of the Weil homomorphism is given. Relations between universal characteristic classes for the regular and the general case are analyzed. In analogy with classical geometry, a natural spectral sequence is introduced and investigated. The appropriate counterpart of the Chern character is constructed, for structures admitting regular connections. Illustrative examples and constructions are presented.

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