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Rigidity problem for lattices in solvable Lie groups

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Abstract

The paper concerns rigidity problem for lattices in simply connected solvable Lie groups. A lattice Γ⊂G is said to be rigid if for any isomorphism ϕ:Γ→Γ′ with another lattice Γ′⊂G there exists an automorphism\(\hat \phi :G \to G\) which extends ϕ. An effective rigidity criterion is proved which generalizes well-known rigidity theorems due to Malcev and Saito. New examples of rigid and nonrigid lattices are constructed. In particular, we construct: a) rigid lattice Γ⊂G which is not Zariski dense in the adjoint representation ofG, b) Zariski dense lattice Γ⊂G which is not rigid, c) rigid virtually nilpotent lattice Γ in a solvable nonnilpotent Lie groupG.

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Authors and Affiliations

  1. Department of Mathematics, Moscow State University, 117234, Moscow, Russia

    A N Starkov

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  1. A N Starkov
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Starkov, A.N. Rigidity problem for lattices in solvable Lie groups. Proc. Indian Acad. Sci. (Math. Sci.) 104, 495–514 (1994). https://doi.org/10.1007/BF02867117

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  • DOI: https://doi.org/10.1007/BF02867117

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