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Journal of Applied Mathematics
Volume 2014 (2014), Article ID 173072, 12 pages
http://dx.doi.org/10.1155/2014/173072
Research Article

Classification of the Quasifiliform Nilpotent Lie Algebras of Dimension 9

1Department of Mechanical Engineering, University of La Rioja, 26004 Logroño, Spain
2Department of Applied Mathematics I, University of Sevilla, 41012 Seville, Spain
3Department of Electrical Engineering, University of La Rioja, 26004 Logroño, Spain

Received 3 November 2013; Accepted 2 January 2014; Published 6 March 2014

Academic Editor: Peter G. L. Leach

Copyright © 2014 Mercedes Pérez et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. H. Georgi, Lie Algebras in Particle Physics: From Isospin to Unified Theories (Frontiers in Physics), Westview Press, Boulder, Colo, USA, 1999.
  2. R. Gilmore, Lie Groups, Lie Algebras, and Some of Their Applications, Dover, New York, NY, USA, 2005. View at MathSciNet
  3. W. A. De Graaf, “Constructing algebraic groups from their Lie algebras,” Journal of Symbolic Computation, vol. 44, no. 9, pp. 1223–1233, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. R. J. Moitsheki and M. D. Mhlongo, “Classical Lie point symmetry analysis of a steady nonlinear one-dimensional fin problem,” Journal of Applied Mathematics, vol. 2012, Article ID 671548, 13 pages, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. K. S. Govinder, “Symbolic implementation of preliminary group classiffication for ordinary differential equations,” Journal of Applied Mathematics, vol. 2013, Article ID 976271, 6 pages, 2013. View at Publisher · View at Google Scholar
  6. M. Goze and Y. Khakimdjanov, Nilpotent Lie Algebras, Kluwer Academic, New York, NY, USA, 1996.
  7. D. Burde, B. Eick, and W. de Graaf, “Computing faithful representations for nilpotent Lie algebras,” Journal of Algebra, vol. 322, no. 3, pp. 602–612, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. J. C. Benjumea, J. Núñez, and F. Tenorio, “Computing the law of a family of solvable Lie algebras,” International Journal of Algebra and Computation, vol. 19, no. 3, pp. 337–345, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. C. Schneider, “A computer-based approach to the classification of nilpotent Lie algebras,” Experimental Mathematics, vol. 14, no. 2, pp. 153–160, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. J. M. Ancochéa-Bermúdez and M. Goze, “Sur la classification des algèbres de Lie nilpotentes de dimension 7,” Comptes Rendus des Séances de l'Académie des Sciences. Série I. Mathématique, vol. 302, no. 17, pp. 611–613, 1986. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. J. M. Ancochéa-Bermúdez and M. Goze, “Classification des algèbres de Lie nilpotentes complexes de dimension 7,” Archiv der Mathematik, vol. 52, no. 2, pp. 175–185, 1989. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. J. M. Ancochéa-Bermúdez and M. Goze, “Classification des algèbres de Lie filiformes de dimension 8,” Archiv der Mathematik, vol. 50, no. 6, pp. 511–525, 1988. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. J. R. Gomez and F. J. Echarte, “Classification of complex filiform nilpotent Lie algebras of dimension 9,” Rendiconti del Seminario della Facoltà di Scienze dell'Università di Cagliari, vol. 61, no. 1, pp. 21–29, 1991. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. F. J. Castro, J. R. Gomez, A. Jiménez-Merchan, N. Nunez, and G. Valeiras, “Determination of law families of fliliform Lie algebres,” in Proceedings of the Workshop of Matricial Analysis and Applications, Vitoria, Spain, 1995.
  15. J. R. Gomez and A. Jiménez-Merchan, “Naturally graded quasi-filiform Lie algebras,” Journal of Algebra, vol. 256, no. 1, pp. 211–228, 2002. View at Google Scholar
  16. L. García-Vergnolle, “Sur les algèbres de Lie quasi-filiformes admettant un tore de dérivations,” Manuscripta Mathematica, vol. 124, no. 4, pp. 489–505, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. M. Vergne, Varieté des algèbres de Lie nilpotentes [Ph.D. thesis], Kluwer Academic, Paris, France, 1966.
  18. M. Vergne, “Cohomologie des algèbres de Lie nilpotentes. Application à l'étude de la variété des algèbres de Lie nilpotentes,” Bulletin de la Société Mathématique de France, vol. 98, pp. 81–116, 1970. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. F. Pérez, Clasificacion de las algebras de lie cuasifiliformes de dimension 9 [Ph.D. thesis], University of Sevilla, Sevilla, Spain, 2007.
  20. G. G. A. Bäuerle and E. A. de Kerf, Lie Algebras Part 1, Studies in Mathematical Physics 1, Elsevier, New York, NY, USA, 1990.
  21. J. C. Benjumea, D. Fernandez, M. C. Márquez, J. Nuñez, and J. A. Vilches, Matemáticas Avanzadas y Estadística para Ciencias e Ingenierías, Secretariado de Publicaciones de la Universidad de Sevilla, Sevilla, Spain, 2006.
  22. J. R. Sendra, S. Perez-Diaz, J. Sendra, and C. Villarino, Introducción a la Computación Simbólica y Facilidades Maple, Addlink Media, 2009.
  23. M. Goze, “Perturbations of Lie algebra structures,” in Deformation Theory of Algebras and Structures and Applications, M. Hazewinkel and M. Gerstenhaber, Eds., pp. 265–355, Kluwer, New York, NY, USA, 1988. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet