Abstract
On any symplectic manifold, we show the existence of a closed star product by constructing a Weyl manifold. There is also an involutive anti-automorphism on a Weyl manifold. By using this, a complexification relating to a quaternion ring is given.
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References
Bayen, F., Flato, M., Fronsdal, C., Lichnerowiz, A., and Sternheimer, D., Deformation theory and quantization I, Ann. Phys. 111, 61–110 (1978).
Connes, A., Flato, M. and Sternheimer, D., Closed star products and cyclic cohomology, Lett. Math. Phys. 24, 1–12 (1992).
Karasev, M. V. and Nazaikinskii, V. E., On the quantization of rapidly oscillating symbols, Math. U.S.S.R. Izv. 34, 737–764 (1978).
Moyal, J. E., Qunatum mechanics as a statistical theory, Proc. Cambridge Phil. Soc. 45, 99–124 (1949).
Omori, H., Infinite Dimensional Lie Groups (in Japanese), Kinokuni-ya, 1978.
Omori, H., Maeda, Y., and Yoshioka, A., Weyl manifolds and deformation quantization, Adv. in Math. 85, 224–255 (1991).
DeWilde, M. and Lecomte, P. B., Existence of star-products and of formal deformations of the Poisson Lie algebra of arbitrary symplectic manifolds, Lett. Math. Phys. 7, 487–496 (1983).