Skip to main content
SpringerLink
Log in

A Characterization of Twin Buildings by Twin Apartments

  • Published:
Geometriae Dedicata Aims and scope Submit manuscript

Abstract

A twin building is a pair of buildings along with a certain ’codistance' between chambers of one building, and chambers of the other. All spherical buildings can be regarded as twin buildings (such a building is twinned with itself in a natural way), and the aim of this paper is to give a definition of twin buildings along the lines that Tits originally gave for spherical buildings. This alternative approach via apartments has been used by the first author in studying some group actions on twin buildings.

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

References

  1. Abramenko, P.: Group actions on twin buildings, Bull. Belg. Math. Soc. 3 (1996), 391–406.

    Google Scholar 

  2. Abramenko, P.: Twin Buildings and Applications to S-Arithmetic Groups, Lecture Notes in Math. 1641, Springer-Verlag, New York, 1996.

    Google Scholar 

  3. Brown, K. S.: Buildings, Springer-Verlag, New York, 1989.

    Google Scholar 

  4. Ronan, M.: Lectures on Buildings, Perspect. Math. 7, Academic Press, New York, 1989.

    Google Scholar 

  5. Ronan, M.: Local isometries of twin buildings (to appear).

  6. Ronan, M. and Tits, J.: Twin trees I. Invent. Math. 116 (1994), 463–479.

    Google Scholar 

  7. Tits, J.: Buildings of Spherical Type and Finite BN Pairs, Lecture Notes in Math. 386, Springer-Verlag, New York, 1974.

    Google Scholar 

  8. Tits, J.: A local approach to buildings, In: The Geometric Vein (Coxeter Festschrift), Springer-Verlag, New York, 1981, pp. 519–547.

    Google Scholar 

  9. Tits, J.: Buildings and group amalgamations, In: Groups (St. Andrews 1985), London Math. Soc. Lecture Notes Ser. 121, Cambridge University Press, 1986, pp. 110–127.

  10. Tits, J.: Uniqueness and presentation of Kac–Moody groups over fields, J. Algebra 105 (1987), 542–573.

    Google Scholar 

  11. Tits, J.: Résumé de cours, Ann. College France, 89e anné, 1988–1989, 81–95.

  12. Tits, J.: Résumé de cours, Ann. College France, 90e année, 1989–1990, 87–103.

  13. Tits, J.: Twin buildings and groups of Kac–Moody type, In: Proc. of a Conference on Groups, Combinatorics and Geometry (Durham 1990), London Math. Soc. Lecture Note Ser. 165, Cambridge University Press, 1992, pp. 249–286.

Download references

Author information

Authors and Affiliations

  1. SFB 343 (Mathematik), Universität Bielefeld, Postfach 10 01 31, D-33501, Bielefeld, Germany; e-mail

    Peter Abramenko

  2. Mathematics Department, University of Illinois at Chicago, 851 S. Morgan (m/c 249), Chicago, IL, 60607, U.S.A. e-mail

    Mark Ronan

Authors
  1. Peter Abramenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mark Ronan
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Abramenko, P., Ronan, M. A Characterization of Twin Buildings by Twin Apartments. Geometriae Dedicata 73, 1–9 (1998). https://doi.org/10.1023/A:1005065400830

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1005065400830

Search

Navigation