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Advances in Mathematical Physics
Volume 2014, Article ID 401238, 9 pages
http://dx.doi.org/10.1155/2014/401238
Research Article

On Generalized Jordan Prederivations and Generalized Prederivations of Lie Superalgebras

School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China

Received 10 May 2014; Revised 29 July 2014; Accepted 19 August 2014; Published 2 September 2014

Academic Editor: Andrei D. Mironov

Copyright © 2014 Yao Ma and Liangyun Chen. 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. G. F. Leger and E. M. Luks, “Generalized derivations of lie algebras,” Journal of Algebra, vol. 228, no. 1, pp. 165–203, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  2. C.-K. Liu and W.-K. Shiue, “Generalized Jordan triple (θ, φ)-derivations on semiprime rings,” Taiwanese Journal of Mathematics, vol. 11, no. 5, pp. 1397–1406, 2007. View at Google Scholar · View at Scopus
  3. A. Najati, “Jordan θ-derivations on Lie triple systems,” Bulletin of the Korean Mathematical Society, vol. 46, no. 3, pp. 435–437, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. Y. Benoist, “Semisimple part o f the algebra of derivations of a nilpotent Lie algebra,” Comptes Rendus de l'Académie des Sciences. Series I. Mathematics, vol. 307, no. 18, pp. 901–904, 1988. View at Google Scholar
  5. I. N. Herstein, Topics in Ring Theory, The University of Chicago Press, Chicago, Ill, USA, 1969. View at MathSciNet
  6. M. Brešar and J. Vukman, “Jordan (Θ,φ)-derivations,” Glasnik Matematicki, vol. 26, no. 1-2, pp. 13–17, 1991. View at Google Scholar
  7. M. Ashraf, A. Ali, and S. Ali, “On Lie ideals and generalized (θ, φ)-derivations in prime rings,” Communications in Algebra, vol. 32, no. 8, pp. 2977–2985, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  8. L. Chen, Y. Ma, and L. Ni, “Generalized derivations of lie color algebras,” Results in Mathematics, vol. 63, no. 3-4, pp. 923–936, 2013. View at Publisher · View at Google Scholar · View at Scopus
  9. A. Najati, “Generalized derivations on Lie triple systems,” Results in Mathematics, vol. 54, no. 1-2, pp. 143–147, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  10. A. Najati, “On generalized Jordan derivations of Lie triple systems,” Czechoslovak Mathematical Journal, vol. 60(135), no. 2, pp. 541–547, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  11. D. Müller, “Isometries of bi-invariant pseudo-Riemannian metrics on Lie groups,” Geometriae Dedicata, vol. 29, no. 1, pp. 65–96, 1989. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. I. Bajo, “Lie algebras admitting non-singular prederivations,” Indagationes Mathematicae: New Series, vol. 8, no. 4, pp. 433–437, 1997. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. W. A. Moens, “A characterisation of nilpotent Lie algebras by invertible LEIbniz-derivations,” Communications in Algebra, vol. 41, no. 7, pp. 2427–2440, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  14. D. Burde, “Affine cohomology classes for filiform Lie algebras,” Contemporary Mathematics, vol. 262, pp. 159–170, 2000. View at Google Scholar
  15. D. Burde, “Lie algebra prederivations and strongly nilpotent Lie algebras,” Communications in Algebra, vol. 30, no. 7, pp. 3157–3175, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  16. D. Burde and W. A. Moens, “Periodic derivations and prederivations of Lie algebras,” Journal of Algebra, vol. 357, pp. 208–221, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  17. P. Ji and L. Wang, “Lie triple derivations of TUHF algebras,” Linear Algebra and Its Applications, vol. 403, no. 1—3, pp. 399–408, 2005. View at Publisher · View at Google Scholar · View at Scopus
  18. C. R. Miers, “Lie triple derivations of von Neumann algebras,” Proceedings of the American Mathematical Society, vol. 71, no. 1, pp. 57–61, 1978. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. H.-T. Wang and Q.-G. Li, “Lie triple derivation of the Lie algebra of strictly upper triangular matrix over a commutative ring,” Linear Algebra and Its Applications, vol. 430, no. 1, pp. 66–77, 2009. View at Publisher · View at Google Scholar · View at Scopus
  20. J. Zhang, B. Wu, and H. Cao, “Lie triple derivations of nest algebras,” Linear Algebra and Its Applications, vol. 416, no. 2-3, pp. 559–567, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  21. M. Brešar, “Jordan mappings of semiprime rings,” Journal of Algebra, vol. 127, no. 1, pp. 218–228, 1989. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus