Translations in certain groups of affine motions

Scheuneman, John

doi:10.1090/S0002-9939-1975-0372120-7

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Translations in certain groups of affine motions
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by John Scheuneman PDF

Proc. Amer. Math. Soc. 47 (1975), 223-228 Request permission

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