Skip to main content
Log in

Geometry of Noncommutative Algebraic Principal Bundles

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

REFERENCES

  1. T. Brzezinski and S. Majid, “Quantum group gauge theory on quantum spaces,” Commun. Math. Phys., 157, 591–638 (1993).

    MathSciNet  Google Scholar 

  2. A. Connes, “Geometrie non-commutative,” Publ. Math. IHES, 62, 41 (1986).

    Google Scholar 

  3. M. Durdevic, “Geometry of quantum principal bundles, I,” Commun. Math. Phys., 175, 457–520 (1996).

    MathSciNet  Google Scholar 

  4. M. Durdevic, “Geometry of quantum principal bundles, II,” Rev. Math. Phys., 9, No.5, 531–603 (1997).

    MathSciNet  Google Scholar 

  5. M. Durdevic, Characteristic classes of quantum principal bundles, Preprint, Inst. Math., UNAM, Mexico (1995).

    Google Scholar 

  6. M. Durdevic, “Quantum principal bundles and Tannaka-Krein duality theory,” Rep. Math. Phys., 38, No.3, 313–324 (1996).

    MathSciNet  Google Scholar 

  7. M. Durdevic, “Differential structures on quantum principal bundles,” Rep. Math. Phys., 41, No.1, 91–115 (1998).

    MathSciNet  Google Scholar 

  8. U. Garow-Watamura, M. Schlieker, S. Watamura, and W. Weich, “Bicovariant differential calculi on quantum groups SU q (n) and SO q (n),” Commun. Math. Phys., 142, 605–641 (1991).

    Google Scholar 

  9. P. M. Hajac, “Strong connections on quantum principal bundles,” Commun. Math. Phys., 182, 579–617 (1996).

    MATH  MathSciNet  Google Scholar 

  10. M. Karoubi, “Homologie cyclique et K-theorie,” Asterisque, 149 (1987).

  11. S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, Vol. II, Interscience Publ., New York-London-Sydney (1969).

    Google Scholar 

  12. H. F. Kreimer, M. Takeuchi, “Hopf algebras and Galois extension of an algebra,” Indiana Univ. Math. J., 30, No.5, 675–692 (1981).

    Article  MathSciNet  Google Scholar 

  13. J.-L. Loday, Cyclic Homology, Grundlehren Math. Wiss., 301, Springer-Verlag, Berlin (1992).

    Google Scholar 

  14. N. Yu. Reshetikhin, L. A. Takhtadzhan, and L. D. Faddeev, “Quantization of Lie groups and Lie algebras,” Algebra Analiz, 1, No.1, 178–206 (1989).

    Google Scholar 

  15. K. Schmudgen and A. Schuler, “Classification of bicovariant differential calculi on quantum groups of type A, B, C, and D,” Commun. Math. Phys., 167, No.2, 635–670 (1995).

    MathSciNet  Google Scholar 

  16. P. Schupp, Quantum groups, noncommutative differential geometry, and applications, Thesis, Univ. of California, Berkeley (1993).

    Google Scholar 

  17. G. I. Sharygin, “Image of the Weyl homomorphism in the case of quantum principal bundles,” Vestn. Mosk. Univ., Ser. 1, Mat., Mekh., 4, 21–27 (2000).

    MATH  MathSciNet  Google Scholar 

  18. G. I. Sharygin, “An obstruction for the existence of connections on bimodules,” Vestn. Mosk. Univ., Ser. 1, Mat., Mekh., 6, 63–65 (2000).

    Google Scholar 

  19. G. I. Sharygin, “Quantum principal bundles, connections, and characteristic classes,” in: Proc. Int Conf. Dedic. to the 70th Anniv. of G. F. Laptev [in Russian], Moscow (1999), p. 58.

  20. M. E. Sweedler, Hopf Algebras, W. A. Benjamin, New York (1969).

    Google Scholar 

  21. S. L. Woronowicz, “Twisted SU(2) group. An example of noncommutative differential calculus,” RIMS, Kyoto Univ., 23, 117–181 (1987).

    MATH  MathSciNet  Google Scholar 

  22. S. L. Woronowicz, “Compact matrix pseudogroups,” Commun. Math. Phys., 111, 613–665 (1987).

    Article  MATH  MathSciNet  Google Scholar 

  23. S. L. Woronowicz, “Differential calculus on compact matrix pseudogroups (quantum groups),” Commun Math. Phys., 122, 125–170 (1989).

    Article  MATH  MathSciNet  Google Scholar 

  24. S. L. Woronowicz, “Tannaka-Krein duality for compact matrix pseudogroups. Twisted SU(n) groups,” Invent. Math., 93, 35–76 (1988).

    Article  MATH  MathSciNet  Google Scholar 

  25. Yu. J. Zhuraev, Characteristic classes of modules over noncommutative algebras, Ph.D. Thesis, Moscow (1988).

  26. Yu. J. Zhuraev, A. S. Mishchenko, and Yu. P. Solov'ev, “On characteristic classes in algebraic K-theory,” Vestn. Mosk. Univ., Ser. 1, Mat., Mekh., 1, 75–76 (1986).

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

__________

Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 19, Topology and Noncommutative Geometry, 2004.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sharygin, G.I. Geometry of Noncommutative Algebraic Principal Bundles. J Math Sci 134, 1911–1982 (2006). https://doi.org/10.1007/s10958-006-0092-z

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-006-0092-z

Keywords

Navigation