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Superrigid Subgroups and Syndetic Hulls in Solvable Lie Groups

In: Rigidity in Dynamics and Geometry

Author

Listed:
  • Dave Witte

    (Oklahoma State University, Department of Mathematics)

Abstract

It is not difficult to see that every group homomorphism from ℤ k to ℝ n extends to a homomorphism from ℝ k to ℝ n . We discuss other examples of discrete subgroups Γ of connected Lie groups G, such that the homomorphisms defined on Γ can (“virtually”) be extended to homomorphisms defined on all of G. For the case where G is solvable, we give a simple proof that Γ has this property if it is Zariski dense. The key ingredient is a result on the existence of syndetic hulls.

Suggested Citation

  • Dave Witte, 2002. "Superrigid Subgroups and Syndetic Hulls in Solvable Lie Groups," Springer Books, in: Marc Burger & Alessandra Iozzi (ed.), Rigidity in Dynamics and Geometry, pages 441-457, Springer.
    • Handle: RePEc:spr:sprchp:978-3-662-04743-9_24
    DOI: 10.1007/978-3-662-04743-9_24
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