Quantum principal bundles and their characteristic classes

Mićo Đurđević

Banach Center Publications (1997)

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

Abstract

top
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.

How to cite

top

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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.