Affine actions on nilpotent Lie groups

DOI10.1515/FORUM.2009.045zbMath1175.22007arXiv0711.4959OpenAlexW2963119938WikidataQ115236437 ScholiaQ115236437MaRDI QIDQ3182461

Sandra Deschamps, Karel Dekimpe, Dietrich Burde

Publication date: 9 October 2009

Published in: Forum Mathematicum (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0711.4959

zbMATH Keywords

Lie algebranilpotent Lie groupunipotent groupsimply transitive affine actionaffine automorphism of nilpotent Lie group

Mathematics Subject Classification ID

Nilpotent and solvable Lie groups (22E25) Global differential geometry (53C99) Solvable, nilpotent (super)algebras (17B30)

Related Items (11)

Simply transitive nil-affine actions of solvable Lie groups ⋮ Commutative post-Lie algebra structures on Lie algebras ⋮ A Zassenhaus conjecture and CPA-structures on simple modular Lie algebras ⋮ Invariant theory of free bicommutative algebras ⋮ Affine actions on Lie groups and post-Lie algebra structures ⋮ Commutative post-Lie algebra structures and linear equations for nilpotent Lie algebras ⋮ Post-Lie algebra structures for nilpotent Lie algebras ⋮ Complete LR-structures on solvable Lie algebras ⋮ Derivation double Lie algebras ⋮ Post-Lie algebra structures on pairs of Lie algebras ⋮ Commutative post-Lie algebra structures on nilpotent Lie algebras and Poisson algebras

Cites Work

• Three-dimensional affine crystallographic groups
• On fundamental groups of complete affinely flat manifolds
• The uniqueness of polynomial crystallographic actions
• Modules for certain Lie algebras of maximal class
• Affine structures on a class of virtually nilpotent groups
• Translations in Certain Groups of Affine Motions
• Semi-simple splittings for solvable Lie groups and polynomial structures
• AFFINE STRUCTURES ON NILMANIFOLDS

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