Skip to main content
SpringerLink
Log in

Comparison of the K-theories of Quillen and Volodin

  • Published:
Journal of Soviet Mathematics Aims and scope Submit manuscript

Abstract

A single proof of coincidence of K-theories of Quillen and Volodin is given for the linear, orthogonal and symplectic cases.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Literature cited

  1. N. Bourbaki, Lie Groups and Algebras. Chapter VI, Hermann, Paris (1965).

    Google Scholar 

  2. I. A. Volodin, “Algebraic K-theory as an extraordinary theory of homologies on categories of associative rings with identity,” Izv. Akad. Nauk SSSR, Ser. Mat.,35, No. 4, 855–873 (1971).

    Google Scholar 

  3. P. Gabriel and M. Zisman, Calculus of Fractions and Homotopy Theory, Springer-Verlag, New York (1967).

    Google Scholar 

  4. I. S. Klein and A. V. Mikhalev, “Unitary Steinberg groups over rings with involutions,” Algebra i Logika,9, No. 5, 510–519 (1970).

    Google Scholar 

  5. J. Milnor, Introduction to Algebraic K-Theory, Princeton Univ. Press, Princeton (1971).

    Google Scholar 

  6. A. I. Nemyshov and Yu. P. Solov'ev, “BN-pairs and Hermitian K-theory,” in: Algebra [in Russian], Mosk. Gos. Univ., Moscow (1982), pp. 102–118.

    Google Scholar 

  7. R. Steinberg, Lectures on Chevalley Groups, Yale Univ., New Haven (1972).

    Google Scholar 

  8. I. A. Panin, “On stabilization for orthogonal and symplectic algebraic K-theory,” Algebra i Analiz,1, No. 3, 172–195 (1989).

    Google Scholar 

Download references

Authors
  1. I. A. Panin
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 175, pp. 93–105, 1989.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Panin, I.A. Comparison of the K-theories of Quillen and Volodin. J Math Sci 57, 3500–3507 (1991). https://doi.org/10.1007/BF01100120

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01100120

Keywords

Search

Navigation