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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the number of abelian left symmetric algebras


Authors: Karel Dekimpe and Veerle Ongenae
Journal: Proc. Amer. Math. Soc. 128 (2000), 3191-3200
MSC (2000): Primary 17A30, 17B30; Secondary 57M60, 53B05
Published electronically: May 11, 2000
MathSciNet review: 1695151
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Abstract:

In this paper we prove that there are infinitely many abelian left symmetric algebras in dimensions $\geq 6$. Equivalently this means that there are, up to affine conjugation, infinitely many simply transitive affine actions of $\mathbb R^k$, for $k\geq 6$. This is a result which is usually credited to A.T. Vasquez, but for which there is no proof in the literature.


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Additional Information

Karel Dekimpe
Affiliation: Katholieke Universiteit Leuven Campus Kortrijk, Universitaire Campus, B-8500 Kortrijk, Belgium
Email: Karel.Dekimpe@kulak.ac.be

Veerle Ongenae
Affiliation: Katholieke Universiteit Leuven Campus Kortrijk, Universitaire Campus, B-8500 Kortrijk, Belgium
Address at time of publication: Department of Pure Mathematics and Computer Algebra, University of Ghent, Galglaan 2, B-9000 Gent, Belgium
Email: vo@cage.rug.ac.be

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05484-8
PII: S 0002-9939(00)05484-8
Keywords: Left symmetric algebra, simply transitive affine action
Received by editor(s): January 11, 1999
Published electronically: May 11, 2000
Additional Notes: The first author is a Research Fellow of the Fund for Scientific Research – Flanders (Belgium) (F.W.O.)
Communicated by: Christopher Croke
Article copyright: © Copyright 2000 American Mathematical Society