On the number of abelian left symmetric algebras
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- by Karel Dekimpe and Veerle Ongenae PDF
- Proc. Amer. Math. Soc. 128 (2000), 3191-3200 Request permission
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.References
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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
- 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
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 3191-3200
- MSC (2000): Primary 17A30, 17B30; Secondary 57M60, 53B05
- DOI: https://doi.org/10.1090/S0002-9939-00-05484-8
- MathSciNet review: 1695151