# Quantum classifying spaces and universal quantum characteristic classes

Banach Center Publications (1997)

- Volume: 40, Issue: 1, page 315-327
- ISSN: 0137-6934

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topĐurđević, Mićo. "Quantum classifying spaces and universal quantum characteristic classes." Banach Center Publications 40.1 (1997): 315-327. <http://eudml.org/doc/252219>.

@article{Đurđević1997,

abstract = {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.},

author = {Đurđević, Mićo},

journal = {Banach Center Publications},

keywords = {quantum principal bundle; quantum classifying space; universal quantum characteristic class; compact matrix quantum group; quantum space; Hopf algebra; -algebra; cohomology algebra; classifying map},

language = {eng},

number = {1},

pages = {315-327},

title = {Quantum classifying spaces and universal quantum characteristic classes},

url = {http://eudml.org/doc/252219},

volume = {40},

year = {1997},

}

TY - JOUR

AU - Đurđević, Mićo

TI - Quantum classifying spaces and universal quantum characteristic classes

JO - Banach Center Publications

PY - 1997

VL - 40

IS - 1

SP - 315

EP - 327

AB - 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.

LA - eng

KW - quantum principal bundle; quantum classifying space; universal quantum characteristic class; compact matrix quantum group; quantum space; Hopf algebra; -algebra; cohomology algebra; classifying map

UR - http://eudml.org/doc/252219

ER -

## References

top- [1] A. Connes, Noncommutative Geometry, Academic Press (1994).
- [2] S. Doplicher, J. E. Roberts, Endomorphisms of C*-algebras, Cross Products and Duality for Compact Groups, Ann Math, 130, 75-119 (1989). Zbl0702.46044
- [3] M. Đurđević, Geometry of Quantum Principal Bundles I, Commun Math Phys 175 (3) 457-521 (1996).
- [4] M. Đurđević, Geometry of Quantum Principal Bundles II-Extended Version, Preprint, Instituto de Matematicas, UNAM, México (1994).
- [5] M. Đurđević, Characteristic Classes of Quantum Principal Bundles, Preprint, Instituto de Matematicas, UNAM, México (1995).
- [6] M. Đurđević, Quantum Principal Bundles and Their Characteristic Classes, this volume, 303-313. Zbl0877.55008
- [7] M. Đurđević, Geometry of Quantum Classifying Spaces, in preparation (1997).
- [8] M. Đurđević, Cyclic Homology for Quantum Classifying Spaces, in preparation (1997).
- [9] J.-L. Loday, Cyclic Homology, A series of Comprehensive Studies in Mathematics 301, Springer-Verlag (1992).
- [10] S. L. Woronowicz, Compact Matrix Pseudogroups, Commun Math Phys 111 613-665 (1987).
- [11] S. L. Woronowicz, Differential Calculus on Compact Matrix Pseudogroups/Quantum Groups, Commun Math Phys 122 125-170 (1989). Zbl0751.58042

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