Translations in certain groups of affine motions
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- by John Scheuneman
- Proc. Amer. Math. Soc. 47 (1975), 223-228
- DOI: https://doi.org/10.1090/S0002-9939-1975-0372120-7
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Abstract:
The purpose of this article is to prove the conjecture of L. Auslander that every nilpotent group of affine motions of ${{\mathbf {R}}^n}$ that is simply transitive on ${{\mathbf {R}}^n}$ has a nontrivial translation in its center. The preliminary result that every such group is unipotent is of independent interest.References
- Armand Borel, Groupes linéaires algébriques, Ann. of Math. (2) 64 (1956), 20–82 (French). MR 93006, DOI 10.2307/1969949
- John Scheuneman, Affine structures on three-step nilpotent Lie algebras, Proc. Amer. Math. Soc. 46 (1974), 451–454. MR 412344, DOI 10.1090/S0002-9939-1974-0412344-2
Bibliographic Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 47 (1975), 223-228
- MSC: Primary 22E25; Secondary 17B30
- DOI: https://doi.org/10.1090/S0002-9939-1975-0372120-7
- MathSciNet review: 0372120