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On the nonrationality of rigid Lie algebras
Author(s):
J.
M. Ancochea
Bermudez;
M.
Goze
Journal:
Proc. Amer. Math. Soc.
127
(1999),
2611-2618.
MSC (1991):
Primary 17Bxx
Posted:
April 23, 1999
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Abstract:
In his thesis, Carles made the following conjecture: Every rigid Lie algebra is defined on the field  . 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  . The goal of this note is to provide a large number of examples of rigid but nonrational and nonreal Lie algebras.
References:
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- 2.
- Ancochea Bermudez, J.M., Goze, M., Le rang du système linéaire des racines d'une algèbre de lie résoluble rigide, Communications in Algebra 20 (1992), 875-887. MR 93a:17006
- 3.
- Ancochea Bermudez, J.M., Goze, M., Algèbres de Lie rigides dont le nilradical est filiforme, C.R.A.Sc.Paris 312 (1991), 21-24. MR 91m:17010
- 4.
- Carles, R., Variété d'algèbres de Lie, Thèse Poitiers 1984.
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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:
10.1090/S0002-9939-99-04824-8
PII:
S 0002-9939(99)04824-8
Keywords:
Rigid Lie algebras
Received by editor(s):
April 19, 1996
Received by editor(s) in revised form:
December 1, 1997
Posted:
April 23, 1999
Communicated by:
Roe Goodman
Copyright of article:
Copyright
1999,
American Mathematical Society
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