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Quantization of a Poisson algebra and polynomials associated to links

Published online by Cambridge University Press:  22 January 2016

Tetsuya Ozawa
Tetsuya Ozawa*
Affiliation:
Department of Mathematics, School of Science, Nagoya University, Chikusa-ku, Nagoya, 464-01, Japan
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A formal quantization of Poisson algebras was discussed by several authors (see for instance Drinfel’d [D]). A formal Lie algebra generated by homotopy classes of loops on a Riemann surface ∑ was obtained by W. Goldman in [G], and its Poisson algebra was quantized, in the sense of Drinfel’d, by Turaev in [T].

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 120 , December 1990 , pp. 113 - 127
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1990

References

[D] Drinfel’d, V. G., Quantum group, in “Proc. of ICM’86”, ICM’86, 1986, pp. 798–820.Google Scholar
[G] Goldman, W., Invariant functions on Lie groups and Hamiltonian flows of surface group representations, Invent. Math., 85 (1986), 263–302.Google Scholar
[R] Reidemeister, N. Y., “Knotentheorie”, Celsea, New York, 1948.Google Scholar
[T] Turaev, V. G., Algebras of loops on surfaces, Algebras of Knots, and Quantization, in “Braid group, knot theory and statistical mecanics, Ed. by Yang, C. N. and Ge”, M. L., World Scientific, Teaneck and London 1989.Google Scholar
[HP] Hoste, J. and Przytycki, J., Homotopy skein modules of orientable 3-manifolds, preprint.Google Scholar