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Polynomial Poly-Vector Fields

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

Frank Klinker

Abstract

Keywords

poly vector field decomposition poisson structure jacobi structure

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

Frank Klinker

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.
There are 17 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Frank Klinker This is me

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

Cite

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