Geometriae Dedicata

, Volume 95, Issue 1, pp 19–58 | Cite as

The Proalgebraic Completion of Rigid Groups

  • Hyman Bass
  • Alexander Lubotzky
  • Andy R. Magid
  • Shahar Mozes

Abstract

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.

finitely generated group linear representation 

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Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Hyman Bass
    • 1
  • Alexander Lubotzky
    • 2
  • Andy R. Magid
    • 3
  • Shahar Mozes
    • 2
  1. 1.Department of MathematicsUniversity of MichiganAnn ArborU.S.A
  2. 2.Department of MathematicsHebrew UniversityJerusalemIsrael
  3. 3.Department of MathematicsUniversity of OklahomaNormanU.S.A

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