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On the number of abelian left symmetric algebras
Author(s):
Karel
Dekimpe;
Veerle
Ongenae
Journal:
Proc. Amer. Math. Soc.
128
(2000),
3191-3200.
MSC (2000):
Primary 17A30, 17B30;
Secondary 57M60, 53B05
Posted:
May 11, 2000
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Abstract:
In this paper we prove that there are infinitely many abelian left symmetric algebras in dimensions  . Equivalently this means that there are, up to affine conjugation, infinitely many simply transitive affine actions of  , for  . 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:
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
Posted:
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 of article:
Copyright
2000,
American Mathematical Society
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