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On the nonrationality of rigid Lie algebras


Authors: J. M. Ancochea Bermudez and M. Goze
Journal: Proc. Amer. Math. Soc. 127 (1999), 2611-2618
MSC (1991): Primary 17Bxx
DOI: https://doi.org/10.1090/S0002-9939-99-04824-8
Published electronically: April 23, 1999
MathSciNet review: 1600089
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Abstract: In his thesis, Carles made the following conjecture: Every rigid Lie algebra is defined on the field $Q$. This was quite an interesting question because a positive answer would give a nice explanation of the fact that simple Lie algebras are defined over $Q$. The goal of this note is to provide a large number of examples of rigid but nonrational and nonreal Lie algebras.


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Additional Information

J. M. Ancochea Bermudez
Affiliation: Universidad Complutense, Facultad de Matematicas, Departamento de geometria y topologia 27000 Madrid, Spain

M. Goze
Affiliation: Université de Haute Alsace, Faculté des Sciences et Techniques, 32, rue du Grillenbreit, F, 68000 Colmar, France
Email: M.Goze@univ-mulhouse.fr

DOI: https://doi.org/10.1090/S0002-9939-99-04824-8
Keywords: Rigid Lie algebras
Received by editor(s): April 19, 1996
Received by editor(s) in revised form: December 1, 1997
Published electronically: April 23, 1999
Communicated by: Roe Goodman
Article copyright: © Copyright 1999 American Mathematical Society