The Auslander conjecture for NIL-affine crystallographic groups.

DOI10.1007/s00208-004-0623-1zbMath1081.20058arXivmath/0409476OpenAlexW2167278722WikidataQ123262583 ScholiaQ123262583MaRDI QIDQ1777256

Sandra Deschamps, Karel Dekimpe, Dietrich Burde

Publication date: 12 May 2005

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0409476

zbMATH Keywords

Auslander conjecturevirtually polycyclic groupsNIL-affine crystallographic groups

Mathematics Subject Classification ID

Solvable groups, supersolvable groups (20F16) Discrete subgroups of Lie groups (22E40) Other geometric groups, including crystallographic groups (20H15) Discontinuous groups of transformations (57S30)

Related Items (10)

Commutative post-Lie algebra structures on Lie algebras ⋮ A Zassenhaus conjecture and CPA-structures on simple modular Lie algebras ⋮ Commutative post-Lie algebra structures and linear equations for nilpotent Lie algebras ⋮ Crystallographic actions on Lie groups and post-Lie algebra structures ⋮ Post-Lie algebra structures for nilpotent Lie algebras ⋮ Post-Lie algebra structures on pairs of Lie algebras ⋮ Rota–Baxter operators and post-Lie algebra structures on semisimple Lie algebras ⋮ Commutative post-Lie algebra structures on Kac–Moody algebras ⋮ Crystallographic actions on contractible algebraic manifolds ⋮ Commutative post-Lie algebra structures on nilpotent Lie algebras and Poisson algebras

Cites Work

• Unnamed Item
• Polycyclic-by-finite groups admit a bounded-degree polynomial structure
• Bieberbach groups and flat manifolds
• On fundamental groups of complete affinely flat manifolds
• On the Zariski closure of the linear part of a properly discontinuous group of affine transformations
• Any virtually polycyclic group admits a NIL-affine crystallographic action.
• A non-affine nilvariety
• The construction of affine structures on virtually nilpotent groups
• Modules for certain Lie algebras of maximal class
• The structure of complete locally affine manifolds
• Flat manifolds with parallel torsion
• Properly discontinuous groups of affine transformations with orthogonal linear part
• AFFINE STRUCTURES ON NILMANIFOLDS
• Properly discontinuous groups of affine transformations: a survey

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