A Poincaré-Birkhoff-Witt theorem for infinite dimensional Lie algebras

Hideki OMORI; Yoshiaki MAEDA; Akira YOSHIOKA

doi:10.2969/jmsj/04610025

Hideki OMORI, Yoshiaki MAEDA, Akira YOSHIOKA

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JOURNAL FREE ACCESS

1994 Volume 46 Issue 1 Pages 25-50

DOI https://doi.org/10.2969/jmsj/04610025

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Published: 1994 Received: June 23, 1992 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: SUBTITLE Details: Wrong : Dedicated to Professor Tsunero Takahashi on his sixtieth birthday

Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : Be) F. A. Berezin, Quantization, Math. USSR-Izv., 8 (1974), 1109-1165.
BK) R. H. Bruck and E. Kleinfeld, The structure of alternative division rings, Proc. Amer. Math. Soc., 2 (1951), 878-890.
CG) M. Cahen and S. Gutt, Regular * representations of Lie algebras, Lett. Math. Phys., 6 (1982), 395-404.
G2) S. Gutt, Some aspects of deformation theory and quantization, Quantum Theories and Geometry, (eds., M. Cahen and M. Flato), Kluwer Academic Publishers, 1988, pp. 77-102.
Ma) Y. Matsushima, Theory of Lie Algebras, (in Japanese) Gendai Suugaku-kouza 15, Kyouritsu Press.
Mc) S. MacLane, Homology, Springer, 1963.
S) R. Schafer, An Introduction to Non Associative Algebras, Academic Press, 1976.
OMY1) H. Omori, Y. Maeda and A. Yoshioka, Weyl manifolds and deformation quantization, Adv. in Math., 85 (1991), 224-255.
OMY2) H. Omori, Y. Maeda and A. Yoshioka, On a construction of deformation quantization of Poisson algebras, Proceedings of the Workshop on Geometry and its applications in honor of Mono Obata, (eds., T. Nagano, H. Omori, Y. Maeda and M. Kanai), World Scientific, 1993, pp. 201-218.
Ve) J. Vey, Déformation du crochet de Poisson sur variété symplectique, Comment. Math. Helv., 50 (1975), 421-454.
VK) Yu. M. Vorob'ev and V. Karasev, Poisson manifolds and the Schouten bracket, Functional Anal. Appl., 22 (1988), 1-9.
W) A. Weinstein, The local structure of Poisson manifolds, J. Differential Geom., 18 (1983), 523-557.

Right : [Be] F. A. Berezin, Quantization, Math. USSR-Izv., 8 (1974), 1109-1165.
[BK] R. H. Bruck and E. Kleinfeld, The structure of alternative division rings, Proc. Amer. Math. Soc., 2 (1951), 878-890.
[CG] M. Cahen and S. Gutt, Regular * representations of Lie algebras, Lett. Math. Phys., 6 (1982), 395-404.
[G2] S. Gutt, Some aspects of deformation theory and quantization, Quantum Theories and Geometry, (eds., M. Cahen and M. Flato), Kluwer Academic Publishers, 1988, pp. 77-102.
[Ma] Y. Matsushima, Theory of Lie Algebras, (in Japanese) Gendai Suugaku-kouza 15, Kyouritsu Press.
[Mc] S. MacLane, Homology, Springer, 1963.
[S] R. Schafer, An Introduction to Non Associative Algebras, Academic Press, 1976.
[OMY1] H. Omori, Y. Maeda and A. Yoshioka, Weyl manifolds and deformation quantization, Adv. in Math., 85 (1991), 224-255.
[OMY2] H. Omori, Y. Maeda and A. Yoshioka, On a construction of deformation quantization of Poisson algebras, Proceedings of the Workshop on Geometry and its applications in honor of Mono Obata, (eds., T. Nagano, H. Omori, Y. Maeda and M. Kanai), World Scientific, 1993, pp. 201-218.
[Ve] J. Vey, Déformation du crochet de Poisson sur variété symplectique, Comment. Math. Helv., 50 (1975), 421-454.
[VK] Yu. M. Vorob'ev and V. Karasev, Poisson manifolds and the Schouten bracket, Functional Anal. Appl., 22 (1988), 1-9.
[W] A. Weinstein, The local structure of Poisson manifolds, J. Differential Geom., 18 (1983), 523-557.

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