Superrigid subgroups and syndetic hulls in solvable Lie groups

Dave Witte

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arXiv · math/0102034

Superrigid subgroups and syndetic hulls in solvable Lie groups

Dave Witte

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Abstract

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

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BibTeX RIS

Dave Witte. 2001-12-25. Superrigid subgroups and syndetic hulls in solvable Lie groups. https://arxiv.org/abs/math/0102034

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