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Proceedings of the American Mathematical Society

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

 

 

Affine structures on three-step nilpotent Lie algebras


Author: John Scheuneman
Journal: Proc. Amer. Math. Soc. 46 (1974), 451-454
MSC: Primary 22E25
DOI: https://doi.org/10.1090/S0002-9939-1974-0412344-2
MathSciNet review: 0412344
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Abstract: As part of the investigation of the parallel between solvable Lie theory and the theory of groups of affine motions, it is proved that every three-step nilpotent Lie algebra admits a faithful representation of a certain special kind. It follows immediately that every three-step nilpotent Lie group which is connected, simply connected, and of dimension $ n$ admits a representation as a simply transitive group of affine motions of $ {R^n}$.


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DOI: https://doi.org/10.1090/S0002-9939-1974-0412344-2
Keywords: Simply transitive group of affine motions
Article copyright: © Copyright 1974 American Mathematical Society