Proper affine actions on semisimple Lie algebras

DOI10.5802/aif.3026zbMath1352.22009arXiv1406.5906OpenAlexW3124324580MaRDI QIDQ332202

Ilia Smilga

Publication date: 27 October 2016

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1406.5906

zbMATH Keywords

Milnor conjecturefree groupaffine groupSchottky groupMargulis invariantdiscrete subgroups of Lie groupsAuslander conjectureflat affine manifoldquasi-translation

Mathematics Subject Classification ID

Linear algebraic groups over finite fields (20G40) Automorphisms, derivations, other operators for Lie algebras and super algebras (17B40) Discrete subgroups of Lie groups (22E40) Classical groups (algebro-geometric aspects) (14L35) Linear algebraic groups over the reals, the complexes, the quaternions (20G20) Other geometric groups, including crystallographic groups (20H15) Simple, semisimple, reductive (super)algebras (17B20)

Related Items

Proper affine actions: a sufficient criterion ⋮ Construction of Milnorian representations ⋮ Margulis multiverse: Infinitesimal rigidity, pressure form and convexity ⋮ Tameness of Margulis space-times with parabolics ⋮ Entropy and affine actions for surface groups ⋮ Proper affine actions for right-angled Coxeter groups ⋮ The pressure metric on the Margulis multiverse

Cites Work

• Unnamed Item
• Margulis spacetimes via the arc complex
• The linear part of an affine group acting properly discontinuously and leaving a quadratic form invariant
• Fundamental domains for properly discontinuous affine groups
• Three-dimensional affine crystallographic groups
• Complete affine locally flat manifolds with free fundamental group
• Fundamental polyhedra for Margulis space-times
• On fundamental groups of complete affinely flat manifolds
• Linear holonomy of Margulis space-times
• On the Zariski closure of the linear part of a properly discontinuous group of affine transformations
• The structure of complete locally affine manifolds
• Free subgroups in linear groups
• Proper actions on reductive homogeneous spaces
• Geometry and topology of complete Lorentz spacetimes of constant curvature
• Lie groups beyond an introduction
• Properly discontinuous groups of affine transformations: a survey