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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ジャーナルフリー

1994 年 46 巻 1 号 p. 25-50

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

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Published: 1994 Received: 1992/06/23 Available on J-STAGE: 2006/10/20 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/10/20 訂正理由: - 訂正箇所: 論文サブタイトル訂正内容: Wrong : Dedicated to Professor Tsunero Takahashi on his sixtieth birthday

訂正日: 2006/10/20 訂正理由: - 訂正箇所: 引用文献情報訂正内容: 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.

訂正日: 2006/10/20 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

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