Quantum classifying spaces and universal quantum characteristic classes

Mićo Đurđević

Banach Center Publications (1997)

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

Abstract

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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.

How to cite

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Đurđević, 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

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  1. [1] A. Connes, Noncommutative Geometry, Academic Press (1994). 
  2. [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. [3] M. Đurđević, Geometry of Quantum Principal Bundles I, Commun Math Phys 175 (3) 457-521 (1996). 
  4. [4] M. Đurđević, Geometry of Quantum Principal Bundles II-Extended Version, Preprint, Instituto de Matematicas, UNAM, México (1994). 
  5. [5] M. Đurđević, Characteristic Classes of Quantum Principal Bundles, Preprint, Instituto de Matematicas, UNAM, México (1995). 
  6. [6] M. Đurđević, Quantum Principal Bundles and Their Characteristic Classes, this volume, 303-313. Zbl0877.55008
  7. [7] M. Đurđević, Geometry of Quantum Classifying Spaces, in preparation (1997). 
  8. [8] M. Đurđević, Cyclic Homology for Quantum Classifying Spaces, in preparation (1997). 
  9. [9] J.-L. Loday, Cyclic Homology, A series of Comprehensive Studies in Mathematics 301, Springer-Verlag (1992). 
  10. [10] S. L. Woronowicz, Compact Matrix Pseudogroups, Commun Math Phys 111 613-665 (1987). 
  11. [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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