Journal of Mathematical Sciences

, Volume 152, Issue 3, pp 372–403 | Cite as

D-differential E-algebras and Steenrod operations in spectral sequences

  • S. V. Lapin


This paper is devoted to the introduction of a D -differential analog of the notion of an E -(co)algebra and to the construction of generalized Steenrod operations in terms of multiplicative spectral sequences. In this paper, we investigate basic homotopy properties of D -differential E -(co)algebras and construct a spectral sequence of a D -differential E -(co)algebra.


Symmetrical Group Spectral Sequence Homology Class Cochain Complex Initial Term 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    J. F. Adams, “On the structure and applications of the Steenrod algebra,” Comm. Math. Helv., 32, 180–214 (1958).MATHCrossRefGoogle Scholar
  2. 2.
    T. V. Kadeishvili, “On the homology theory of fibered spaces,” Usp. Mat. Nauk, 35, 183–188 (1980).MathSciNetGoogle Scholar
  3. 3.
    S. V. Lapin, “The differential perturbations and D -differential modules,” Mat. Sb., 192, No. 11, 55–76 (2001).MathSciNetGoogle Scholar
  4. 4.
    S. V. Lapin, “The differential A -algebras and spectral sequences,” Mat. Sb., 193, No. 1, 119–142 (2002).MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    S. V. Lapin, “The (DA)-modules over (DA)-algebras and spectral sequences,” Izv. RAN Ser. Mat., 66, No. 3, 103–130 (2002).MathSciNetGoogle Scholar
  6. 6.
    J. P. May, “A general algebraic approach to Steenrod operations,” in: Lect. Notes Math., 168, 153–231 (1970).CrossRefMathSciNetGoogle Scholar
  7. 7.
    S. P. Novikov, “On cohomologies of the Steenrod algebra,” Dokl. Akad. Nauk SSSR, 128, No. 5, 893–895 (1959).MATHMathSciNetGoogle Scholar
  8. 8.
    V. A. Smirnov, “On the cochain complex of a topological space,” Mat. Sb., 115, No. 1, 146–158 (1981).MathSciNetGoogle Scholar
  9. 9.
    V. A. Smirnov, “The homotopy theory of coalgebras,” Izv. Akad. Nauk SSSR. Ser. Mat., 49, No. 6, 1302–1321 (1985).MATHMathSciNetGoogle Scholar
  10. 10.
    V. A. Smirnov, “Homologies of B-constructions and co-B-constructions,” Izv. RAN Ser. Mat., 58, No. 4, 80–96 (1994).MATHGoogle Scholar
  11. 11.
    V. A. Smirnov, “Lie algebras over operads and their application in homotopy theory,” Izv. RAN Ser. Mat., 62, No. 3, 121–154 (1998).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2008

Authors and Affiliations

  • S. V. Lapin
    • 1
  1. 1.Ogarev Mordovia State UniversitySaranskRepublic of Mordovia

Personalised recommendations