Generalized Auslander conjecture for nil-affine crystallographic groups
Generalized Auslander conjecture for nil-affine crystallographic groups
Let be a connected and simply connected nilpotent Lie group, and let act properly discontinuously and cocompactly on ; such an action is called nil-affine crystallographic. Generalized Auslander conjecture. Then 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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