Generalized Auslander conjecture for nil-affine crystallographic groups

From papers

Let NN be a connected and simply connected nilpotent Lie group, and let ΓAff(N)\Gamma\subseteq\operatorname{Aff}(N) act properly discontinuously and cocompactly on NN; such an action is called nil-affine crystallographic. Generalized Auslander conjecture. Then Γ\Gamma is virtually polycyclic. This asks for the analogue of the Auslander conjecture for nil-affine crystallographic groups. The source gives Dekimpe's converse result that every virtually polycyclic group admits a nil-affine crystallographic action, unique up to conjugation, but supplies no resolution of this converse implication.

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Sources & referencesView supporting material

Primary source

Dietrich Burde, “Crystallographic actions on Lie groups and post-Lie algebra structures”, arXiv:1909.02797 (2019).

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