Proceedings of the Japan Academy, Series A, Mathematical Sciences

Deformation quantization of Poisson algebras

Hideki Omori, Yoshiaki Maeda, and Akira Yoshioka

Full-text: Open access

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 68, Number 5 (1992), 97-100.

Dates
First available in Project Euclid: 19 November 2007

Permanent link to this document
https://projecteuclid.org/euclid.pja/1195511789

Digital Object Identifier
doi:10.3792/pjaa.68.97

Mathematical Reviews number (MathSciNet)
MR1179113

Zentralblatt MATH identifier
0768.58018

Subjects
Primary: 58H15: Deformations of structures [See also 32Gxx, 58J10]
Secondary: 16S80: Deformations of rings [See also 13D10, 14D15]

Citation

Omori, Hideki; Maeda, Yoshiaki; Yoshioka, Akira. Deformation quantization of Poisson algebras. Proc. Japan Acad. Ser. A Math. Sci. 68 (1992), no. 5, 97--100. doi:10.3792/pjaa.68.97. https://projecteuclid.org/euclid.pja/1195511789


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References

  • [1] M. De Wilde and P. B. Lecomte: Existence of star-products and of formal deformations of the Poisson Lie algebra of arbitrary symplectic manifolds. Lett. Math. Phys., 7, 487-496 (1983).
  • [2] A. Lichnerowicz: Les varietes de Poisson et leurs algebres de Lie associees. J. Diff. Geom., 12, 253-300 (1977).
  • [3] S. MacLane: Homology. Springer (1963).
  • [4] H. Omori, Y. Maeda and A. Yoshioka: Weyl manifolds and deformation quantization. Advances in Math., 85, 224-255 (1991).
  • [5] M. Riefel: C*-algebras associated with irrational rotations. Pacific J. Math., 95(2), 415-429 (1981).
  • [6] Yu. M. Vorob'ev and V. Karasev: Poisson manifolds and the Schouten bracket. Functional Anal. Appl., 22, 1-9 (1988).