SciELO - Scientific Electronic Library Online

 
vol.31 número1Half-Sweep Geometric Mean Iterative Method for the Repeated Simpson Solution of Second Kind Linear Fredholm Integral Equations índice de autoresíndice de materiabúsqueda de artículos
Home Pagelista alfabética de revistas  

Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

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

http://dx.doi.org/10.4067/S0716-09172012000100008 

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

 


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

 


REFERENCES

[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,

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