# Quantum principal bundles and their characteristic classes

Banach Center Publications (1997)

- Volume: 40, Issue: 1, page 303-313
- ISSN: 0137-6934

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topĐurđević, Mićo. "Quantum principal bundles and their characteristic classes." Banach Center Publications 40.1 (1997): 303-313. <http://eudml.org/doc/252194>.

@article{Đurđević1997,

abstract = {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.},

author = {Đurđević, Mićo},

journal = {Banach Center Publications},

keywords = {quantum principal bundle; quantum characteristic class; Weil homomorphism; compact matrix quantum group; quantum space; Hopf algebra; -algebra; spectral sequence; cohomology},

language = {eng},

number = {1},

pages = {303-313},

title = {Quantum principal bundles and their characteristic classes},

url = {http://eudml.org/doc/252194},

volume = {40},

year = {1997},

}

TY - JOUR

AU - Đurđević, Mićo

TI - Quantum principal bundles and their characteristic classes

JO - Banach Center Publications

PY - 1997

VL - 40

IS - 1

SP - 303

EP - 313

AB - 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.

LA - eng

KW - quantum principal bundle; quantum characteristic class; Weil homomorphism; compact matrix quantum group; quantum space; Hopf algebra; -algebra; spectral sequence; cohomology

UR - http://eudml.org/doc/252194

ER -

## References

top- [1] R. Bott & W. Tu, Differential Forms in Algebraic Topology, Springer-Verlag New-York (1982). Zbl0496.55001
- [2] A. Connes, Non-commutative differential geometry, Extrait des Publications Mathématiques, IHES 62 (1986).
- [3] A. Connes, Noncommutative Geometry, Academic Press (1994).
- [4] M. Đurđević, Geometry of Quantum Principal Bundles I, Commun Math Phys 175 (3) 457-521 (1996).
- [5] M. Đurđević, Geometry of Quantum Principal Bundles II-Extended Version, Preprint, Instituto de Matematicas, UNAM, México (1994).
- [6] M. Đurđević, Characteristic Classes of Quantum Principal Bundles, Preprint, Instituto de Matematicas, UNAM, México (1995).
- [7] M. Đurđević, General Frame Structures on Quantum Principal Bundles, Preprint, Instituto de Matematicas, UNAM, México (1995).
- [8] S. Kobayashi & K. Nomizu, Foundations of Differential Geometry, Interscience Publishers New York, London (1963). Zbl0119.37502
- [9] S. L. Woronowicz, Compact Matrix Pseudogroups, Commun Math Phys 111 613-665 (1987).
- [10] S. L. Woronowicz, Differential Calculus on Compact Matrix Pseudogroups/ Quantum Groups, Commun Math Phys 122 125-170 (1989). Zbl0751.58042