Superrigid Subgroups and Syndetic Hulls in Solvable Lie Groups

Dave Witte ()
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Dave Witte: Oklahoma State University, Department of Mathematics

A chapter in Rigidity in Dynamics and Geometry, 2002, pp 441-457 from Springer

Abstract: 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.

Keywords: Compact Subgroup; Solvable Group; Closed Subgroup; Discrete Subgroup; Maximal Compact Subgroup (search for similar items in EconPapers)
Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-662-04743-9_24

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DOI: 10.1007/978-3-662-04743-9_24

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