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ISRN Algebra
Volume 2011 (2011), Article ID 381875, 11 pages
http://dx.doi.org/10.5402/2011/381875
Research Article

π‘‡βˆ—πœƒ-Extensions of 𝑛-Lie Algebras

College of Mathematics and Computer Science, Hebei University, Baoding 071002, China

Received 28 May 2011; Accepted 6 July 2011

Academic Editors: W. de Graaf and A. Zimmermann

Copyright Β© 2011 Ruipu Bai and Ying Li. 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. Y. Nambu, β€œGeneralized Hamiltonian dynamics,” Physical Review D, vol. 7, pp. 2405–2412, 1973. View at Google Scholar Β· View at Zentralblatt MATH
  2. L. Takhtajan, β€œOn foundation of the generalized Nambu mechanics,” Communications in Mathematical Physics, vol. 160, no. 2, pp. 295–315, 1994. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
  3. J. Bagger and N. Lambert, β€œGauge symmetry and supersymmetry of multiple M2-branes,” Physical Review D, vol. 77, no. 6, Article ID 065008, 2008. View at Google Scholar
  4. P.-M. Ho, R.-C. Hou, and Y. Matsuo, β€œLie 3-algebra and multiple M2-branes,” Journal of High Energy Physics A, no. 6, 2008. View at Publisher Β· View at Google Scholar
  5. G. Papadopoulos, β€œM2-branes, 3-Lie algebras and PlΓΌcker relations,” Journal of High Energy Physics A, no. 5, 2008. View at Publisher Β· View at Google Scholar
  6. V. T. Filippov, β€œnβ€”Lie algebras,” SibirskiΔ­ MatematicheskiΔ­ Zhurnal, vol. 26, no. 6, pp. 126–140, 1985. View at Google Scholar Β· View at Zentralblatt MATH
  7. S. Kasymov, β€œOn a theory of n-Lie algebras,” Algebra i Logika, vol. 26, no. 3, pp. 277–297, 1987. View at Google Scholar
  8. W. Ling, On the structure of nβ€”Lie algebras, Dissertation, University-GHS-Siegen, Siegen, Germany, 1993.
  9. J. AzcΓ‘rraga and J. Izquierdo, β€œn-ary algebras: a review with applications,” Journal of Physics A, vol. 43, Article ID 293001, 2010. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
  10. A. Pozhidaev, β€œRepresentations of vector product n-Lie algebras,” Communications in Algebra, vol. 32, no. 9, pp. 3315–3326, 2004. View at Google Scholar
  11. M. Goze, N. Goze, and E. Remm, β€œnβ€”Lie algebras,” African Journal of Mathematical Physics, vol. 8, no. 1, pp. 17–28, 2010. View at Google Scholar Β· View at Zentralblatt MATH
  12. R. Bai, C. Bai, and J. Wang, β€œRealizations of 3-Lie algebras,” Journal of Mathematical Physics, vol. 51, no. 6, Article ID 063505, 2010. View at Publisher Β· View at Google Scholar
  13. R. Bai, C. Shen, and Y. Zhang, β€œ3-Lie algebras with an ideal N,” Linear Algebra and its Applications, vol. 431, no. 5–7, pp. 673–700, 2009. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
  14. R. Bai and G. Song, β€œThe classification of six-dimensional 4-Lie algebras,” Journal of Physics A, vol. 42, no. 3, Article ID 035207, 2009. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
  15. M. Bordemann, β€œNondegenerate invariant bilinear forms on nonassociative algebras,” Acta Mathematica Universitatis Comenianae, vol. 66, no. 2, pp. 151–201, 1997. View at Google Scholar Β· View at Zentralblatt MATH
  16. J. Figueroa-O'Farrill, β€œMetric Lie n-algebras and double extensions,” arXiv: 0806.3534.
  17. R. Bai, W. Wu, and Y. Li, β€œModule extensions of 3-Lie algebras,” Linear and Multilinear Algebra, 2011. In press.