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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) vol.31 no.1 Antofagasta mar. 2012 

Proyecciones Journal of Mathematics Vol. 31, No 1, pp. 81-90, March 2012. Universidad Católica del Norte Antofagasta - Chile

On an algorithm for finding derivations of Lie algebras *

Víctor Ayala

Universidad Católica del Norte, Chile

Eyüp Kizil

Universidade de Sao Paulo, Brasil

Ivan de Azevedo Tribuzy

Universidade Federal de Amazonas, Brasil



Let g be an arbitrary finite dimensional Lie algebra over the field R. We give as an additional alternative a detailed overview of an algorithm for finding derivations of g since such procedures are often of interest.

AMS classification : 16W25; 93B29; 93B05

Key words : Derivations ofLie algebras; Linear control system; Null controllability



[1] V. Ayala and J. Tirao, Linear control systems on Lie groups and controllability, in:Proceedings of the American Mathematical Society, Series: Symposia in Pure Mathematics, Vol. 64, (1999).

[2] E. Beck, B. Kolman and I.N. Stewart, Computing the structure of a Lie algebra, in:R.E.Beck and B. Kolman, editors, Non-associative rings and algebras, Academic press, pp. 167-188, (1977).         [ Links ]

[3] W. A. de Graaf, Lie algebras: Theory and Algorithms, North-Holland Mathematical Library, (2000).

[4] G. F. Leger, A note on the derivations of Lie algebras, Proc. Amer. Math. Soc. 4, pp. 511-514, (1953).

[5] D. Leites and G. Post, Cohomology to compute, Proceedings of the thirdconferenceonComputersandMathematics, pp. 73-81, (1989).         [ Links ]

[6] A. O. Nielsen, Unitary representations and coadjoint orbits of low dimensional nilpotent Lie groups, Queen's Papers in Pure and Applied Mathematics 63, (1983).

[7] S. Togo, Derivations of Lie algebras. J. Sci. Hiroshima Univ. Ser. A-1-Math 28pp. 133-158, (1964).         [ Links ]

[8] V.S. Varadaradjan, Lie groups, Lie algebras and Their representations, Prentice-Hall, (1974).

Victor Ayala

Departamento de Matemáticas Universidad Catolica del Norte Casilla 1280, Antofagasta,


e-mail : Eyiip Kizil

Instituto de Ciencias Matematicas e de Computação. Universidade de Sao Paulo.

Cx. Postal 668. 13.560-970,

Sãao Carlos-SP, Brasil

e-mail : and

Ivan de Azevedo Tribuzy

Instituto de Ciencias Exatas. Universidade Federal de Amazonas. Manaus, Brasil

e-mail :

*Research partially supported by Conicyt Proyecto Fondecyt N 1100375

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