The Auslander conjecture for groups leaving a form of signature \((n-2,2)\) invariant.

DOI10.1007/BF02775430zbMath1091.20032OpenAlexW2054796732WikidataQ123281499 ScholiaQ123281499MaRDI QIDQ814147

Gregory A. Margulis, Herbert Abels, G. A. Soifer

Publication date: 6 February 2006

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02775430

zbMATH Keywords

orthogonal groupsaffine crystallographic groupsvirtually solvable groupsAuslander conjecture

Mathematics Subject Classification ID

Unimodular groups, congruence subgroups (group-theoretic aspects) (20H05) Discrete subgroups of Lie groups (22E40) Other geometric groups, including crystallographic groups (20H15) Discontinuous groups of transformations (57S30) Affine differential geometry (53A15) Other special differential geometries (53A40)

Related Items (5)

Properly discontinuous group actions on affine homogeneous spaces ⋮ Affine semigroups acting properly discontinuously on a hyperbolic space ⋮ Proper affine actions for right-angled Coxeter groups ⋮ Crystallographic actions on Lie groups and post-Lie algebra structures ⋮ Representations having vectors fixed by a Levi subgroup associated to a real form

Cites Work

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• The fundamental group of a compact flat Lorentz space form is virtually polycyclic
• Transitive and quasitransitive actions of affine groups preserving a generalized Lorentz-structure
• Three-dimensional affine crystallographic groups
• On the Zariski closure of the linear part of a properly discontinuous group of affine transformations
• Existence of irreducible \(\mathbb R\)-regular elements in Zariski-dense subgroups
• Semigroups containing proximal linear maps
• Properly discontinuous groups of affine transformations with orthogonal linear part
• Properly discontinuous groups of affine transformations: a survey

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