ArticleOriginal scientific text

Title

Quantum classifying spaces and universal quantum characteristic classes

Authors 1

Affiliations

  1. Instituto de Matematicas, UNAM, Area de la Investigacion Cientifica, Circuito Exterior, Ciudad Universitaria, México DF, CP 04510, Mexico

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.

Bibliography

  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).
  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.
  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).
Pages:
315-327
Main language of publication
English
Published
1997
Exact and natural sciences