Acta Mathematica

The serre spectral sequence of a noncommutative fibration for de Rham cohomology

Edwin J. Beggs and Tamasz Brzeziński

Full-text: Open access

Article information

Source
Acta Math., Volume 195, Number 2 (2005), 155-196.

Dates
Received: 26 September 2005
First available in Project Euclid: 31 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.acta/1485891781

Digital Object Identifier
doi:10.1007/BF02588079

Mathematical Reviews number (MathSciNet)
MR2233688

Zentralblatt MATH identifier
1130.46044

Rights
2005 © Institut Mittag-Leffler

Citation

Beggs, Edwin J.; Brzeziński, Tamasz. The serre spectral sequence of a noncommutative fibration for de Rham cohomology. Acta Math. 195 (2005), no. 2, 155--196. doi:10.1007/BF02588079. https://projecteuclid.org/euclid.acta/1485891781


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References

  • Beggs, E. J., Braiding and exponentiating noncommutative vector fields. Preprint, 2003. arXiv:math.QA/0306094.
  • Beggs, E. J., & Brzeziński, T., The van Est spectral sequence for Hopf algebras. Int. J. Geom. Methods Mod. Phys. 1 (2004), 33–48.
  • Bénabou, J., Introduction to bicategories, in Reports of the Midwest Category Seminar, pp. 1–77. Lecture Notes in Math., 47. Springer, Berlin, 1967.
  • Brzeziński, T., Remarks on bicovariant differential calculi and exterior Hopf algebras. Lett. Math. Phys., 27 (1993), 287–300.
  • Brzeziński, T., El Kaoutit, L. & Gómez-Torrecillas, J., The bicategories of corings. To appear in J. Pure Appl. Algebra. arXiv:math.RA/0408042.
  • Brzeziński, T., & Majid, S., Quantum group gauge theory on quantum spaces. Comm. Math. Phys., 157 (1993), 591–638; Erratum, Ibid. Brzeziński, T. & Majid, S., Quantum group gauge theory on quantum spaces. Comm. Math. Phys., 167 (1995), 235.
  • Brzeziński, T., & Wisbauer, R., Corings and Comodules. London Math. Soc. Lecture Note Ser., 309, Cambridge Univ. Press Cambridge, 2003.
  • Caenepeel, S., Militaru, G., & Zhu, S., Frobenius and Separable Functors for Generalized Module Categories and Nonlinear Equations. Lecture Notes in Math., 1787. Springer, Berlin, 2002.
  • Connes, A., Noncommutative Geometry. Academic Press, San Diego, CA, 1994.
  • Evans, D. E., & Kawahigashi, Y., Quantum Symmetries on Operator Algebras. Oxford Univ. Press, New York, 1998.
  • Heckenberger, I., & Schüler, A., de Rham cohomology and Hodge decomposition for quantum groups. Proc. London Math. Soc., 83 (2001), 743–768.
  • Kontsevich, M., & Rosenberg, A. L., Noncommutative smooth spaces, in The Gelfand Mathematical Seminars, 1996–99, pp. 85–108. Gelfand Math. Sem., Birkhäuser, Boston, MA, 2000.
  • Lack, S., & Street, R., The formal theory of monads, II. J. Pure Appl. Algebra, 175 (2002), 243–265.
  • McCleary, J., A User's Guide to Spectral Sequences, 2nd edition. Cambridge Stud. Adv. Math., 58, Cambridge Univ. Press, Cambridge, 2001.
  • Madore, J., An Introduction to Noncommutative Differential Geometry and Its Physical Applications, 2nd edition. London Math. Soc. Lecture Note Ser., 257, Cambridge Univ. Press, Cambridge, 1999.
  • Majid, S., Noncommutative Riemannian and spin geometry of the standard q-sphere. Comm. Math. Phys., 256 (2005), 255–285.
  • Milnor, J. W., & Moore, J. C., On the structure of Hopf algebras. Ann. of Math., 81 (1965), 211–264.
  • Podleś, P., Quantum spheres. Lett. Math. Phys., 14 (1987), 193–202.
  • Rojter, A. V., Matrix problems and representations of BOCS's, in Representation Theory, I. (Ottawa, ON, 1979), pp. 288–324. Lecture Notes in Math., 831, Springer, Berlin-New York, 1980.
  • Schneider, H.-J., Principal homogenous spaces for arbitrary Hopf algebras. Israel J. Math., 72 (1990), 167–195.
  • Street, R., The formal theory of monads. J. Pure Appl. Algebra, 2 (1972), 149–168.
  • Sweedler, M. E., Integrals for Hopf algebras. Ann. of Math., 89 (1969), 323–335.
  • Woronowicz, S. L., Twisted SU(2) group. An example of a noncommutative differential calculus. Publ. Res. Inst. Math. Sci., 23 (1987), 117–181.
  • Woronowicz, S. L., Differential calculus on compact matrix pseudogroups (quantum groups), Comm. Math. Phys., 122 (1989), 125–170.