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Advances in Mathematical Physics
Volume 2015, Article ID 250570, 8 pages
http://dx.doi.org/10.1155/2015/250570
Research Article

Simple Modules for Modular Lie Superalgebras , , and

1School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China
2School of Applied Sciences, Jilin Teachers Institute of Engineering and Technology, Changchun 130052, China

Received 13 April 2015; Revised 28 June 2015; Accepted 30 June 2015

Academic Editor: Andrei D. Mironov

Copyright © 2015 Zhu Wei 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. V. G. Kac, “Classification of infinite-dimensional simple linearly compact Lie superalgebras,” Advances in Mathematics, vol. 139, no. 1, pp. 1–55, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  2. I. Shchepochkina, “The five exceptional simple Lie superalgebras of vector fields and their fourteen regradings,” Representation Theory, vol. 3, pp. 373–415, 1999. View at Publisher · View at Google Scholar · View at MathSciNet
  3. I. Shchepochkina and G. Post, “Explicit bracket in an exceptional simple Lie superalgebra,” International Journal of Algebra and Computation, vol. 8, no. 4, pp. 479–495, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  4. G. Benkart, T. Gregory, and A. Premet, The Recognition Theorem for Graded Lie Algebras in Prime Characteristic, American Mathematical Society, 2009.
  5. H. Strade, Simple Lie Algebras over Fields of Positive Characteristic. I–III, De Gruyter Expositions in Mathematics, Walter de Gruyter, Berlin, Germany, 2004.
  6. S. Bouarroudj, P. Grozman, and D. Leites, “Classification of finite dimensional modular lie superalgebras with indecomposable Cartan matrix,” Symmetry, Integrability and Geometry: Methods and Applications, vol. 5, article 060, 63 pages, 2009. View at Publisher · View at Google Scholar
  7. S. Buarrudzh, P. Y. Grozman, and D. A. Leites, “New simple modular Lie superalgebras as generalized prolongs,” Functional Analysis and Its Applications, vol. 42, no. 3, pp. 161–168, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. Y. C. Su, “Composition factors of Kac modules for the general linear Lie superalgebras,” Mathematische Zeitschrift, vol. 252, no. 4, pp. 731–754, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. Y. C. Su and L. S. Zhu, “Representations of the derivation algebra of the localization of the quantum plane at q=-1,” Communications in Algebra, vol. 33, pp. 4375–4382, 2005. View at Google Scholar
  10. Y. C. Su, “Classification of quasifinite modules over Lie algebras of matrix differential operators on the circle,” Proceedings of the American Mathematical Society, vol. 133, no. 7, pp. 1949–1957, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. Y. C. Su and J. H. Zhou, “A class of nongraded simple Lie algebras,” Communications in Algebra, vol. 32, no. 6, pp. 2365–2376, 2004. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. Y. Su and J. Zhou, “Some representations of nongraded Lie algebras of generalized Witt type,” Journal of Algebra, vol. 246, no. 2, pp. 721–738, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  13. Y. Z. Zhang, “Z-Graded module of Lie superalgebra H(n) of Cartan type,” Chinese Science Bulletin, vol. 41, pp. 813–817, 1996. View at Google Scholar
  14. Y. Z. Zhang, “Z-Graded module of Lie superalgebra W(n) and S(n) of Cartan type,” Chinese Science Bulletin, vol. 41, pp. 589–592, 1996. View at Google Scholar
  15. R. R. Holmes, “Simple restricted modules for the restricted contact Lie algebras,” Proceedings of the American Mathematical Society, vol. 116, no. 2, pp. 329–337, 1992. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. R. R. Holmes, “Cartan invariants for the restricted toral rank two contact Lie algebra,” Indagationes Mathematicae, vol. 5, no. 3, pp. 291–305, 1994. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  17. R. R. Holmes, “Dimensions of the simple restricted modules for the restricted contact Lie algebra,” Journal of Algebra, vol. 170, no. 2, pp. 504–525, 1994. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  18. R. R. Holmes, “Simple restricted modules for the restricted Hamiltonian algebra,” Journal of Algebra, vol. 199, no. 1, pp. 229–261, 1998. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  19. G. Y. Shen, “Graded modules of graede Lie algebras of Cartan type(I)—mixed product of modules,” Scientia Sinica (Series A), vol. 29, pp. 570–581, 1986. View at Google Scholar
  20. G. Y. Shen, “Graded modules of graded Lie algebras of Cartan type(II)-positive and negative graded modules,” Scientia Sinica.—Series A: Mathematical, Physical, Astronomical &; Technical Sciences, vol. 29, no. 10, pp. 1009–1019, 1986. View at Google Scholar · View at MathSciNet
  21. G. Y. Shen, “Graded modules of graded Lie algebras of Cartan type(III)—irreducible modules,” Chinese Annals of Mathematics Series B, vol. 9, no. 4, pp. 404–417, 1988. View at Google Scholar · View at MathSciNet
  22. N. H. Hu, “The graded modules for the graded contact Cartan algebras,” Communications in Algebra, vol. 22, no. 11, pp. 4475–4497, 1994. View at Publisher · View at Google Scholar · View at MathSciNet
  23. B. Shu, “The generalized restricted representations of graded Lie algebras of Cartan type,” Journal of Algebra, vol. 194, no. 1, pp. 157–177, 1997. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  24. W. D. Liu, “Induced modules of restricted Lie superalgebras,” Northeastern Mathematical Journal, vol. 21, pp. 54–60, 2005. View at Google Scholar
  25. Y. Wang and Y. Z. Zhang, “The property of a p-mapping on a restricted Lie superalgebra,” Journal of Northeast Normal University, vol. 32, pp. 106–110, 2000 (Chinese). View at Google Scholar
  26. Y. Z. Zhang, “Finite-dimensional Lie superalgebras of Cartan type over fields of prime characteristic,” Chinese Science Bulletin, vol. 42, no. 9, pp. 720–724, 1997. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  27. B. Xin, Lie superalgebra K(n) [Dissertation for the Master's Degree], Northeast Normal University, Changchun, China, 2003.