On an Algorithm for Finding Derivations of Lie Algebras

Authors

  • Víctor Ayala Universidad Católica del Norte.
  • Eyup Kizil Universidade de São Paulo.
  • Ivan De Azevedo Tribuzy Universidade Federal de Manaus.

DOI:

https://doi.org/10.4067/S0716-09172012000100008

Keywords:

Derivations of Lie algebras, linear control system, null controllability, derivaciones de álgebras de Lie, sistemas de control lineal, controlabilidad nula.

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.

Author Biographies

Víctor Ayala, Universidad Católica del Norte.

Departamento de Matemáticas.

Eyup Kizil, Universidade de São Paulo.

Instituto de Ciencias Matematicas e de Computacao.

Ivan De Azevedo Tribuzy, Universidade Federal de Manaus.

Instituto de Ciências Exatas.

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).

[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 third conference on Computers and Mathematics, pp. 73-81, (1989).

[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).

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

Published

2012-01-29

How to Cite

[1]
V. Ayala, E. Kizil, and I. De Azevedo Tribuzy, “On an Algorithm for Finding Derivations of Lie Algebras”, Proyecciones (Antofagasta, On line), vol. 31, no. 1, pp. 81-90, Jan. 2012.

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