The proalgebraic completion of rigid groups

Hyman Bass*, Alexander Lubotzky, Andy R. Magid, Shahar Mozes

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

23 Scopus citations


A finitely generated group Γ is called representation rigid (briefly, rigid) if for every n, Γ has only finitely many classes of simple ℂ representations in dimension n. Examples include higher rank S-arithmetic groups. By Margulis super rigidity, the latter have a stronger property: they are representation super rigid; i.e., their proalgebraic completion is finite dimensional. We construct examples of nonlinear rigid groups which are not super rigid, and which exhibit every possible type of infinite dimensionality. Whether linear representation rigid groups are super rigid remains an open question.

Original languageAmerican English
Pages (from-to)19-58
Number of pages40
JournalGeometriae Dedicata
Issue number1
StatePublished - 2002

Bibliographical note

Funding Information:
The authors collectively, individually, and in various subsets, gratefully acknowledge support at various times from the United States Israel Binational Science Foundation, the Israel Science Foundation, the United States National Security Agency and National Science Foundation, Hebrew University, the University of Oklahoma, Columbia University and the University of Michigan.


  • Finitely generated group
  • Linear representation


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