Proyecciones Journal of Mathematics Vol. 31, N^o 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

 

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ABSTRACT

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

 

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REFERENCES

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[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).

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[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,

Chile

e-mail : vayala@ucn.cl 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 : kizil@icmc.usp.br and

Ivan de Azevedo Tribuzy

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

e-mail : ivan@argo.com.br

*Research partially supported by Conicyt Proyecto Fondecyt N 1100375