Skip to main content
SpringerLink
Log in

Stability of the Haagerup property under graph products

  • Published:
Archiv der Mathematik Aims and scope Submit manuscript

Abstract

In this paper, we prove that any graph product of finitely many groups, all satisfying the Haagerup property (or Gromov’s a-T-menability) also satisfies the Haagerup property.

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

Fig. 1
Fig. 2

Similar content being viewed by others

References

  1. Antolín, Y., Dreesen, D.: The Haagerup property is stable under graph products. arXiv:1305.6748 (2013)

  2. Akemann, C.A., Walter, M.E.: Unbounded negative definite functions. Canadian J. Math. 33(4), 862–871 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  3. Bekka, M.E.B., Cherix, P.-A., Valette, A.: Proper affine isometric actions of amenable groups. In: Novikov Conjectures, Index Theorems and Rigidity, vol. 2 (Oberwolfach, 1993), pp. 1–4. London Math. Soc. Lecture Note Ser., 227. Cambridge Univ. Press, Cambridge (1995)

  4. Brown, N.P., Ozawa, N.: \(C^{*}\)-Algebras and Finite-Dimensional Approximations. Graduate Studies in Mathematics, 88. American Mathematical Society, Providence, RI (2008)

  5. Choda, M.: Group factors of the Haagerup type. Proc. Japan Acad. Ser. A Math. Sci. 59(5), 174–177 (1983)

  6. Chatterji, I., Niblo, G.: From wall spaces to CAT (0) cube complexes. Internat. J. Algebra Comput. 15, 875–885 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  7. Cherix, P-A, Cowling, M., Jolissaint, P., Julg, P., Valette, A.: Groups with the Haagerup Property. Gromov’s a-T-menability. Progress in Mathematics, 197. Birkhäuser, Basel (2001)

  8. Green, E.R.: Graph products of groups. PhD Thesis, University of Leeds (1990)

  9. Gromov, M.: Asymptotic invariants of infinite groups. In: Geometric Group Theory, vol. 2 (Sussex, 1991), pp. 1–295. London Math. Soc. Lecture Note Ser., 182. Cambridge Univ. Press, Cambridge (1993)

  10. Haagerup, U.: An example of a nonnuclear \(C^*\)-algebra, which has the metric approximation property. Invent. Math. 50(3), 279–293 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  11. de la Harpe, P., Valette, A.: La propriété (T) de Kazhdan pour les groupes localement compacts (avec un appendice de Marc Burger). Astérisque No. 175, 158 pp. (1989)

  12. Kazhdan, D.A.: Connection of the dual space of a group with the structure of its closed subgroups. Funct. Anal. Appl. 1, 63–65 (1967)

    Article  MathSciNet  MATH  Google Scholar 

  13. Niblo, G.A., Reeves, L.: Groups acting on CAT(0) cube complexes. Geom. Topol. 1, 7 pp. (1997)

  14. Paterson, A.L.T.: Amenability. Mathematical Surveys and Monographs, 29. American Mathematical Society, Providence, RI (1988)

  15. Reckwerdt, E.: Weak amenability is stable under graph products. J. Lond. Math. Soc. 96(1), 133–155 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  16. Schoenberg, I.J.: Metric spaces and completely monotone functions. Ann. of Math. (2), 39(4), 811–841 (1938)

Download references

Acknowledgements

PSG was supported by the CSIR Fellowship [File No. 08/155(0066)/2019-EMR-I], Govt. of India. SD acknowledges the infrastructural support provided by the Dept. of Mathematics, Presidency University, through the DST-FIST [File No. SR/FST/MS-I/2019/41].

Author information

Authors and Affiliations

  1. Department of Mathematics, Presidency University, 86/1, College Street, Kolkata-73, India

    Shubhabrata Das & Partha Sarathi Ghosh

Authors
  1. Shubhabrata Das
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Partha Sarathi Ghosh
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shubhabrata Das.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Das, S., Ghosh, P.S. Stability of the Haagerup property under graph products. Arch. Math. 121, 257–265 (2023). https://doi.org/10.1007/s00013-023-01904-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00013-023-01904-8

Keywords

Mathematics Subject Classification

Search

Navigation