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Polynomial Poly-Vector Fields

Year 2009, Volume: 2 Issue: 1, 55 - 73, 30.04.2009

Abstract

References

  • [1] Azcarrage, J.A., Perelomov, A.M. and Perez Bueno, J.C., The Schouten-Nijenhuis bracket, cohomology and generalized Poisson structures. J. Phys. A, Math. Gen., 29(24):7993-8009, 1996.
  • [2] Azcarrage, J.A., Perelomov, A.M. and Perez Bueno, J.C., Generalized Poisson structures. arXiv: hep-th/9611221 v2, 1996.
  • [3] Bhaskara, K.H. and Rama, K., Quadratic Poisson structures. J. Math. Phys., 32(9):2319- 2322, 1991.
  • [4] Cari~nena, J. F., Ibort, A., Marmo, G. and Perelomov, A. M., On the geometry of Lie algebras and Poisson tensors. J. Phys. A, Math. Gen., 27(22):7425-7449, 1994. x
  • [5] Dufour, Jean-Paul and Haraki, Abdeljalil, Rotationels et structures de Poisson quadratiques. C. R. Acad. Sci. Paris, Ser.I, (312):137-140, 1991.
  • [6] Fulton, William and Harris, Joe, Representation Theory. Graduate Texts in Mathematics 129. Springer-Verlag, New York, 1991.
  • [7] Grabowski, J., Marmo, G. and Perelomov, A. M., Poisson structures: towards a classi¯cation. Modern Phys. Lett. A, 8(18):1719-1733, 1993.
  • [8] Klinker, Frank, Quadratic Poisson structures in dimension four. Available at http://www.mathematik.tu-dortmund.de/∼klinker.
  • [9] Kobayashi, Shoshichi and Nomizu, Katsumi, Foundations of Differential Geometry. Vol. I. Wiley Classics Library. John Wiley & Sons Inc., New York, 1996.
  • [10] Koszul, Jean-Louis, Crochet de Schouten-Nijenhuis et cohomologie. (Schouten-Nijenhuis bracket and cohomology). In Elie Cartan et les mathematiques d'aujourd'hui, The mathematical heritage of Elie Cartan, Semin. Lyon 1984, Asterisque, No.Hors Ser. 1985, 257-271,1985.
  • [11] Lin, Qian, Liu, Zhangju and Sheng, Yunhe, Quadratic deformations of Lie-Poisson structures. Lett. Math. Phys., 83(3):217-229, 2008.
  • [12] Liu, Zhangju and Xu, Ping, On quadratic Poisson structures. Lett. Math. Phys., 26(1):33-42, 1992.
  • [13] Malek, F. and Shafei Deh Abad, A., Homogeneous Poisson structures. Bull. Aust. Math. Soc., 54(2):203-210, 1996.
  • [14] Manchon, D., Masmoudi, M. and Roux, A., On quantization of quadratic Poisson structures. Comm. Math. Phys., 22(1):121-130, 2002.
  • [15] Perez Bueno, J.C., Generalized Jacobi structures. J. Phys. A, Math. Gen., 30(18):6509-6515, 1996.
  • [16] Petalidou, Fani, On a new relation between Jacobi and homogeneous Poisson manifolds. J. Phys. A, Math. Gen., 35:2505-2518, 2002.
  • [17] Sheng, Yunhe , Linear Poisson structures on R4. Journal of Geometry and Physics, 57(11) Pages 2398-2410, 2007.
Year 2009, Volume: 2 Issue: 1, 55 - 73, 30.04.2009

Abstract

References

  • [1] Azcarrage, J.A., Perelomov, A.M. and Perez Bueno, J.C., The Schouten-Nijenhuis bracket, cohomology and generalized Poisson structures. J. Phys. A, Math. Gen., 29(24):7993-8009, 1996.
  • [2] Azcarrage, J.A., Perelomov, A.M. and Perez Bueno, J.C., Generalized Poisson structures. arXiv: hep-th/9611221 v2, 1996.
  • [3] Bhaskara, K.H. and Rama, K., Quadratic Poisson structures. J. Math. Phys., 32(9):2319- 2322, 1991.
  • [4] Cari~nena, J. F., Ibort, A., Marmo, G. and Perelomov, A. M., On the geometry of Lie algebras and Poisson tensors. J. Phys. A, Math. Gen., 27(22):7425-7449, 1994. x
  • [5] Dufour, Jean-Paul and Haraki, Abdeljalil, Rotationels et structures de Poisson quadratiques. C. R. Acad. Sci. Paris, Ser.I, (312):137-140, 1991.
  • [6] Fulton, William and Harris, Joe, Representation Theory. Graduate Texts in Mathematics 129. Springer-Verlag, New York, 1991.
  • [7] Grabowski, J., Marmo, G. and Perelomov, A. M., Poisson structures: towards a classi¯cation. Modern Phys. Lett. A, 8(18):1719-1733, 1993.
  • [8] Klinker, Frank, Quadratic Poisson structures in dimension four. Available at http://www.mathematik.tu-dortmund.de/∼klinker.
  • [9] Kobayashi, Shoshichi and Nomizu, Katsumi, Foundations of Differential Geometry. Vol. I. Wiley Classics Library. John Wiley & Sons Inc., New York, 1996.
  • [10] Koszul, Jean-Louis, Crochet de Schouten-Nijenhuis et cohomologie. (Schouten-Nijenhuis bracket and cohomology). In Elie Cartan et les mathematiques d'aujourd'hui, The mathematical heritage of Elie Cartan, Semin. Lyon 1984, Asterisque, No.Hors Ser. 1985, 257-271,1985.
  • [11] Lin, Qian, Liu, Zhangju and Sheng, Yunhe, Quadratic deformations of Lie-Poisson structures. Lett. Math. Phys., 83(3):217-229, 2008.
  • [12] Liu, Zhangju and Xu, Ping, On quadratic Poisson structures. Lett. Math. Phys., 26(1):33-42, 1992.
  • [13] Malek, F. and Shafei Deh Abad, A., Homogeneous Poisson structures. Bull. Aust. Math. Soc., 54(2):203-210, 1996.
  • [14] Manchon, D., Masmoudi, M. and Roux, A., On quantization of quadratic Poisson structures. Comm. Math. Phys., 22(1):121-130, 2002.
  • [15] Perez Bueno, J.C., Generalized Jacobi structures. J. Phys. A, Math. Gen., 30(18):6509-6515, 1996.
  • [16] Petalidou, Fani, On a new relation between Jacobi and homogeneous Poisson manifolds. J. Phys. A, Math. Gen., 35:2505-2518, 2002.
  • [17] Sheng, Yunhe , Linear Poisson structures on R4. Journal of Geometry and Physics, 57(11) Pages 2398-2410, 2007.

Details

Primary Language English
Journal Section Research Article
Authors

Frank KLİNKER This is me

Publication Date April 30, 2009
Published in Issue Year 2009 Volume: 2 Issue: 1

Cite

APA KLİNKER, F. (2009). Polynomial Poly-Vector Fields. International Electronic Journal of Geometry, 2(1), 55-73.
AMA KLİNKER F. Polynomial Poly-Vector Fields. Int. Electron. J. Geom. April 2009;2(1):55-73.
Chicago KLİNKER, Frank. “Polynomial Poly-Vector Fields”. International Electronic Journal of Geometry 2, no. 1 (April 2009): 55-73.
EndNote KLİNKER F (April 1, 2009) Polynomial Poly-Vector Fields. International Electronic Journal of Geometry 2 1 55–73.
IEEE F. KLİNKER, “Polynomial Poly-Vector Fields”, Int. Electron. J. Geom., vol. 2, no. 1, pp. 55–73, 2009.
ISNAD KLİNKER, Frank. “Polynomial Poly-Vector Fields”. International Electronic Journal of Geometry 2/1 (April 2009), 55-73.
JAMA KLİNKER F. Polynomial Poly-Vector Fields. Int. Electron. J. Geom. 2009;2:55–73.
MLA KLİNKER, Frank. “Polynomial Poly-Vector Fields”. International Electronic Journal of Geometry, vol. 2, no. 1, 2009, pp. 55-73.
Vancouver KLİNKER F. Polynomial Poly-Vector Fields. Int. Electron. J. Geom. 2009;2(1):55-73.